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Kit Ian KOU, Anna高潔欣 Associate Professor |
Academic Qualification
- Ph.D. in Mathematics, UM (2005)
- M.Sc. in Mathematics, UM (1999)
- B.Ed. in Mathematics, UM (1996)
Google Scholar Address
Working Experience
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Associate Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao. |
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Assistant Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao. |
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Research Fellow, Clare Hall, University of Cambridge, Cambridge United Kingdom |
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Assistant Professor, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao. |
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Lecturer, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao. |
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Teaching Assistant, Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao. |
Teaching
M.Sc. and Ph.D Courses
- Topics in Analysis (IMAT016)
- Reading course (IMAT012)
- Clifford Analysis (IMAT005)
- Advance in Mathematics (IMSE002)
- Advanced Engineering Mathematics (MATH801)
B.Sc. Courses
- Mathematical Analysis I (MATH101)
- Mathematical Analysis II (MATB221)
- Finite Mathematics (EDUC106)
- Mathematical Analysis III (MATH200/ EDUC352)
- Mathematical Analysis IV (MATH201)
- Numerical Methods and Computation (MATH207)
- Probability and Statistics (EDUC212/254)
- Probability (MATB213)
- Multivariate Calculus (EDUC252)
- Ordinary Differential Equations (EDUC320)
- Mathematical Analysis III (EDUC352)
- Complex Analysis (EDUC354/MATB311)
- Mathematical Physics Methods (EDUC414)
- Partial Differential Equations (EDUC446)
- Seminar (EDUC491)
Research
Research Interests
- Fourier analysis
- Quaternion and Clifford analysis
- Windowed linear canonical analysis
- Shannon sampling theorems
- Harmonic analysis in Euclidean spaces
- Signal and image analysis
Research Projects and Grants
External Grants:
- 22/07/2016-21/07/2019: Macau Government FDCT/031/2016/A1. Quaternion Linear Canonical Transforms and Applications, funded by the FDCT. Principal Investigator.
- 01/01/2016-31/12/2018: National Natural Foundation for Youth Scholars No. 11501015, 半空间中次调和函数的Matseav 定理, funded by the NSFC, Co-Principal Investigator.
- 01/01/2015-31/12/2017: National Natural Foundation for Youth Scholars No. 11401606, The related topics about spheroidal wave functions in quaternion analysis (四元数分析中椭球体波函数相关问题的研究), funded by the NSFC,UMacau Research Institute, Zhuhai, Guandong, China. Principal Investigator.
- 03/10/2013-02/10/2016: Macau Government FDCT/099/2012/A3. Generalized spheroidal wave functions and applications in Quaternion Analysis, funded by the FDCT. Principal Investigator.
- 05/10/2012-04/10/2014: Macau Government FDCT/094/2011/A. Clifford analysis and applications, funded by the FDCT. Principal Investigator.
- 01/01/2010-31/12/2012: National Natural Foundation for Youth Scholars No.10901166, Clifford analysis methods in higher dimensional space, by Y. Yang (PI) and K.I. Kou (Co-PI), funded by the NSFC.
Internal Grants (Principal Investigator)
- 16/7/2015-15/7/2018:MYRG2015-00058-FST. The Application of Quaternions to Some Signal Problems, funded by the Research Committee of UM.Principle Investigator.
- 13/03/2014-12/03/2017:MRG012/KKI/2014/FST.Genearlized pheroidal wave functions and applications in Quaternion Analysis, funded by the Research Committee of UM. Principle Investigator.
- May 2013-June 2016: MYRG099 (Y1-L2)-FST13-KKI. Fourier Analysis and Applications, funded by the Research Committee of UM. Principle Investigator.
- January 2013-December 2014: MRG002/KKI/2013/FST. Clifford Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
- June 2011-April 2015: MYRG142(Y3-L2)-FST11-KKI. Time-Frequency Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
- January 2010-December 2011: RG076/09-10S/11R/KKI/FST. Applied Complex and Harmonic Analysis in Euclidean Space, funded by the Research Committee of UM. Principal Investigator.
- January 2007 – June 2009: RG070/06-07S/09T/KKI/FST. Hardy Spaces of Monogenic Functions & Applications, funded by the Research Committee of University of Macau. Principal Investigator.
- January 2005 – December 2006: RG059/05-06S/QT/FST. Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
- January 2003 – December 2005: RG091/04-05S/C117. Clifford Analysis Methods in Harmonic Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
- January 2002 – December 2002: RG055/01-02S/QT/FST. (a) Monogenic Sinc Function and Applications; (b) Harmonic Analysis on the Unit Spheres in Higher Dimensional Euclidean Space, funded by the Research Committee of University of Macau, Co-Principal Investigator.
- January 2000 – December 2001: RG024/00-01S/QT/FST. Higher Dimensional Sinc Methods and Applications in Partial Differential Equations, funded by the Research Committee of University of Macau, , two years. Co-Principal Investigator.
Academic Activities
Academic Visiting and Delivering Lectures in Mathematical Institutions
Belgium:
- Ghent University (18-23 June 2006, Frank Sommen, Fred Brackex)
China P.R:
- Beijing Normal University, Beijing, China (8-15 August, 2012, Guan Tie Deng)
- Xiamen University, Xiamen (8 – 14 August, 2005, Chun Hui Qiu; 20 – 25 December, 2012, Chun Hui Qiu)
Hong Kong:
- The Chinese University of Hong Kong, Hong Kong (July 1998, Raymond Chan)
Japan:
- International Christian University, Tokyo (2-9 Feb, 2014, Eckhard Hitzer)
Malaysia:
- The institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia (20-26 Dec 2013)
Portugal:
- Aveiro University, Aveiro (23-29 June 2006, Paula Cerejeiras, Uwe Kaehler)
Taiwan:
- Department of Electrical Engineering, National Taiwan University, Taiwan (27 Dec 2013-1 Jan 2014, Jian-Jiun Ding)
- Notional Center for Theoretical Sciences Mathematics Division, Hsinchu, Taiwan. (1-7 July 2014, Der-Chen Chang)
Thailand:
- King Mongkut’s University of Technology Thonburi, Bangkok Thailand (23-31 July, 2014, Thiradet Jiarasuksakun)
United Kingdom:
- University of Cambridge, Cambridge (Clare Hall, 15 Jan -15 July, 2006, A. F. Beardon)
Academic Visitors Invited Supported By My Research Grants:
Australia:
- 2009: Alan McIntosh (Harmonic Analysis, PDEs, Operator Theory), Macquarie University, the Australian National University (to University of Macau)
Belgium:
- 2007: Fred Brackx (Clifford Analysis), Ghent University (to University of Macau)
- 2007: Hennie De Schepper (Clifford Analysis), Ghent University (to University of Macau)
China P.R.:
- 2011, 2012, 2013, 2014: Yan YANG (Clifford Analysis), Sun Yat-Sen University, Guangzhou
- 2012: Yan Hui ZHANG (Complex Analysis), Beijing Technology and Business University, Beijing (to University of Macau)
- 2013, 2014: Ming Sheng LIU (Complex Analysis), South China Normal University, Guangzhou, P. R. China.
- 2014: Luo Qing LI (Signal Analysis), Hubei University, Wuhan, China
- 2014: Yang LIU (Clifford Analysis and Control Theory), Zhejiang Normal University, Jinhua, China
- 2014: Jun Feng XU (Complex Analysis), Wuyi University, Jiangmen, China
- 2015: Yong Hui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, China
Japan:
- 2014: Eckhard Hitzer (Clifford Analysis), International Christian University, Tokyo, Japan
- 2015: (Wavelet Analysis)
Portugal:
- 2007, 2008: Palua Cerejeiras and Uwe Kaehler (Clifford Analysis), University of Aveiro, Aveiro
- 2011, 2012, 2013: Joao Morais (Quaternion Analysis), University of Aveiro, Aveiro
Conferences Attended:
- The 22nd international conference on finite or infinite dimensional complex analysis and applications, 08/08/2014 to 11/08/2014, on the campus of Dongguk University, Gyeongju, Korea.
- 2014 NCTS Workshop on Geometric and Singular Analysis, July 3-4, 2014, Notional Center for Theoretical Sciences Mathematics Division, Hsinchu, Taiwan.
- The Sixth International Congress of Chinese Mathematicians (ICCM 2013). Opening ceremony: July 14, 2013, in the Grand Ballroom of the Grand Hotel, Taipei; Lectures and invited talks: July 15 to July 19, 2013, on the campus of National Taiwan University.
- Harmonic Analysis and its Applications, Jinhua, China, 12-16 October, 2012.
- International Conference on Several Complex Variables Analysis, Henan, China, 16-21 August, 2012.
- The 20th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Hanoi, Vietnam, 29 July-3 August, 2012
- The 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011), G-Hotels, Halkidiki, Greece, 19-25 September 2011
- The 18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, the local organization committee, University of Macau, Macau, 13-17 August 2010
- Symposium on Hyper-Complex Analysis, University of Macau, Macau, 4-8 December 2006
- Function Theories in Higher Dimensions, Institute of Mathematics, Tampere University of Technology, Tampere, Finland, 12-16 June 2006
- Workshop on the recent developments of the Hilbert-Huang Transform methodology and its applications, National Central University, Chungli, Taiwan, 15-17 March 2006
- International Conference on Several Complex Variables, USTC, Hefei Anhui, P. R. of China, June 2005
- Fourth ISAAC (International Society for Analysis, its Applications and Computation) Congress 2003, Toronto, Canada, August 2003
- ICM 2002 International Congress of Mathematicians, Beijing, China, August 2002
- International Conference on Clifford Analysis and Its Applications, Macau, August 2002
- ICCA 6th International Conference on Clifford Algebras and Their Applications, Cookeville, Tennessee, USA, May 2002
- The Center for Mathematics and its Applications National Research Symposium — Banach Spaces, Operators and Algebras, Canberra, Australia, January 2001
- International Congress of Chinese Mathematicians (ICCM), Beijing, China, December 1998
- The Eighth International Congress on Computational and Applied Mathematics (ICCAM 98), Leuven, Belgium, August 1998
Ph.D. students and their thesis topics:
- Graduated
- Cui-Ming Zou (Sept 2013-January 2017). Theory and Applications of Spheroidal Wave Quaternionic Signal. (Principle supervisor)
- Xiao-Xiao Hu (August 2014-July 2017). Spheroidal Functions in Higher-Dimensional Spaces. (Principle supervisor)
- Zhen-Feng Cai (January 2015- January 2018). Quaternion Differential Equations and Applications. (Principle supervisor)
- On going
- Dong Cheng (since 9/2015). (Principle supervisor)
- Wen-Shen Bi (since 9/2015). (Principle supervisor)
- Wan Kai Liu (since 9/2016). (Principle supervisor)
Master students and their thesis topics:
- Graduated
- Yue-Lin Liu (2009). The linear canonical transform and generalized Hilbert transform with applications in signal processing.
- Rui-Hui Xu (2011). Windowed linear canonical transform and its applications.Jian-Yu Ou (2013). Uncertainty principles for quaternionic linear canonical transform and applications.
- Le-Ping Liang (2013). Paley Wiener theorem under linear canonical transform of slice monogenic functions
- Ze-Zhen Cao (2013). Linear canonical transform and applications.
- Ka Man Lei (2014). A tighter uncertainty principle for hypercomplex signals in the linear canonical transform domains.
- Dong Cheng (2015). The generalized sampling expansions associated with quaternion Fourier transform
- Xiao Jun Li (2016). Linear canonical transform in time-frequency analysis.
Post-doctoral and Research Associate Fellows and their Major Research Areas
- 2010, 2012, 2013: Joao MORAIS (Hyper-complex and Clifford Analysis), University of Aveiro, Portugal.
- 2012, 2013, 2014: Ming Sheng LIU (Complex Analysis), South China Normal University, Guangzhou, P. R. China.
- 2012, 2013, 2014:Yan YANG (Clifford Analysis and Signal Analysis), Sun Yat-Sen University, Guangzhou, P. R. China.
- 2013, 2014: Yang LIU (Signal and Control Theory), Zhejiang Normal University, Jinhua, P. R. China.
- 2014: Hong LI (Signal and Data Analysis), Huazhong University of Science and Technology. P. R. China.
- 2014, 2015: Jun Ming LIU (Complex and Signal Analysis), Shantou University, P. R. China.
- 2014: Jun Feng XU (Complex and Signal Analysis), Wuyi University, Jiangmen, P. R. China.
- 2015: Ming Sheng LIU (Quaternion Analysis), South China Normal University, Gauangzhou, P.R. China; Yonghui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, P. R. China.
- 2016: Ming Sheng LIU (Quaternion Analysis), South China Normal University, Gauangzhou, P.R. China; Yonghui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, P. R. China.
Publications
- Z. Cai, K.I. Kou,Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients, Qualitative Theory of Dynamical Systems, 2017. Page 1-12. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- B. Li, Y. Liu, K.I. Kou and L. Yu, Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks, IEEE Transactions on Cybernetics, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- D. Cheng, K.I. Kou, Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions, Adv. Appl. Clifford Algebras, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
- K.I. Kou, J. Liu, Which Linear Operators Preserve Outer Functions? Indagationes Mathematicae, 23 August, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
- J. Chu, S. Heidarkhani, K.I. Kou, and A. Salari, Weak Solutions and Energy Estimates for a Degenerate Nonlocal Problem Involving Sub-linear Nonlinearities, J. Korean Math. Soc. 54 (2017), No. 5, pp. 1573-1594. (NSFC11401606, MYRG2015, FDCT099)
- C. Zou, K.I. Kou and J. Morais, Prolate spheroidal wave functions associated with the quaternionic Fourier transform, Mathematical Methods in Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
- D Zhang, K.I. Kou, Y Liu, J Cao, Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field, Neural Networks, 2017. (NSFC11401606, MYRG2015, FDCT099)
- J. Li and K.I. Kou, Dynamics of Traveling Wave Solutions to a New Highly Nonlinear Shallow Water Wave Equation, International Journal of Bifurcation and Chaos, 27 (03), 1750044, 2017. (NSFC11401606, MYRG2015, FDCT099, FDCT031)
- Y. Zhang, K.I. Kou, Integral representation and estimation of harmonic functions in the quaternionic half space, Mathematical Methods in the Applied Sciences, 27 April, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- Y. Zhang, K.I. Kou, G. Deng, T. Qian, The generalized Matsave theorem on grwth of subharmonic functions admitting a lower bound in Rn, Complex Variables and Elliptic Equations, 62(5), 642-653, 2017. (FDCT099)
- Z. Cai and K.I. Kou, Laplace transform: a new approach in solving linear quaternion differential equations, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- D. Cheng and K.I. Kou, Generalized Sampling Expansions Associated with Quaternion Fourier Transform, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- C. Zou, K.I. Kou, J. Morais, Prolate Spheroidal Wave Functions Associated with the Quaternionic Fourier Transform, Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- Y. Yang, K.I. Kou, C. Zou. Edge detection methods based on modified differential phase congruency of monogenic signal, Multidimensional Systems and Signal Processing, 2017: 1-21. (NSFC11401606, MYRG2015, FDCT031, FDCT099)
- K.I. Kou, Yang~Y, Zou~C. Uncertainty Principle for Measurable Sets and Signal Recovery in Quaternion Domains, to appear in Mathematical Methods in the Applied Sciences, 2017. (NSFC11401606, MYRG2015, FDCT094, FDCT099)
- X. Hu and K.I. Kou. Quaternion Fourier and linear canonical inversion theorems. Mathematical Methods in the Applied Sciences (2016). (NSFC11401606, MYRG2015, FDCT099)
- X. Fan, K.I. Kou and M. Liu, Quaternion Wigner–Ville distribution associated with the linear canonical transforms, Signal Processing, 130 (2017), 129-141. (NSFC11401606, MYRG2015, FDCT099)
- K.I. Kou and J. Li, Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schr¨odinger Equation, Int. J. Bifurcation and Chaos 26 (6) 1650106 (2016)[22 pages] (NSFC11401606, MYRG2015,MYRG099, FDCT094, FDCT099)
- Dong, B., K. I. Kou., Qian, T., & Sabadini, I. (2016). On the inversion of Fueter’s theorem. Journal of Geometry and Physics, 108, 102-116. (MYRG2015)
- K. I. Kou, Yijun Lou, and Yong-Hui Xia, Zeros of a Class of transcendental Equation with Application to Bifurcation of DDE, Int. J. Bifurcation and Chaos 26, 1650062 (2016) [14 pages] DOI:http://dx.doi.org/10.1142/S0218127416500620(NSFC10901166, MYRG099, MYRG2015, FDCT094, FDCT099)
- Y. Xia, L. Chen, K. I. Kou, D. O’Regan, Hölder Regularity of Grobman–Hartman Theorem for Dynamic Equations on Measure Chains, Bulletin of the Malaysian Mathematical Sciences Society, pp 1-28, First online: 12 May 2016 (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- C. Zou, K. I. Kou, and Y. Wang, Quaternion Collaborative and Sparse Representation with Application to Color Face Recognition, IEEE Transactions on Image Processing, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- K. I. Kou, Ming-Sheng Liu and Shu-Zhen Tao,Herglotz’s theorem and quaternion series of positive term, Mathematical Methods in the Applied Sciences, 2016, 39(18): 5607-5618. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- K. I. Kou, M. Liu, J. Morais, C. Zou, Envelope Detection Using Generalized Analytic Signal in 2D QLCT Domains, Multidimensional Systems and Signal Process, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099) DOI :10.1007/s11045-016-0410-7.
- K.I. Kou and H. Li, Greedy adaptive decomposition of signals based on nonlinear Fourier atoms, International Journal of Wavelets, Multiresolution and Information Processing, 2016.(NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- Y. Songy, H. Li, J. Wang, K. I. Kou, Multiple One-Dimensional Embedding Clustering Scheme for Hyperspectral Image Classification, International Journal of Wavelets, Multiresolution and Information Processing, 14 (2), 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- J. Morais and K. I. Kou, Constructing Prolate Spheroidal Quaternion Wave Functions on the Sphere, Mathematical Methods in the Applied Sciences, 2016. (NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- Y. Yang and K.I. Kou, Novel uncertainty principles associated with 2D quaternion Fourier transforms, Integral Transforms and Special Functions, 27 (3), 213-226, 2016.(NSFC11401606, MYRG099, MYRG2015, FDCT094, FDCT099)
- K. I. Kou, Y. Liu, D. Zhang and Y. Tu, Ensemble control of linear systems with parameter uncertainties, International Journal of Control, 27 (3), 213-226, 2016. (NSFC11401606, FDCT094, FDCT099, MYRG099, MYRG2015))
- W Zhang, KI Kou, J Lou, Y Liu, Observer based consensus for nonlinear multi-agent systems with communication failures, Neurocomputing, Vol. 173, 1034-1043. (NSFC11401606, MYRG099, MYRG142, FDCT094, FDCT099)
- K. I. Kou, J. Ou and J. Morais, Uncertainty principles associated with quaternionic linear canonical transforms, Mathematical Methods in the Applied Sciences, Vol. 39, 10, 2722–2736 July (2016). (MYRG099, MYRG2015, FDCT094, FDCT099)
- J. Morais, M.A. Pérez-de la Rosa, K.I. Kou, Computational Geometric and Boundary Value Properties of Oblate Spheroidal Quaternionic Wave Functions, Wave Motion, 57 (2015) 112-128. (MYRG142, FDCT094)
- J. Morais, H.M. Nguyen, K.I. Kou, On 3D Orthogonal Prolate Spheroidal Monogenics, Mathematical Methods in the Applied Sciences. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- M. Liu, K.I. Kou, J. Morais and P. Dang, Sharper Uncertainty Principles for the Windowed Fourier Transform, Journal of Modern Optics, 62 (1), 46-55, 2015. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- Y. Zhang, G. Deng, K.I. Kou, Asymptotic behavior of fractional aplacians in the half space, Applied Mathematics and Computation 254, 125-132, 2015. (MYRG099, MYRG142, FDCT094, FDCT099)
- L. Chen, K.I. Kou, M. Liu, Pitt’s inequality and the uncertainty principle associated with the quaternion Fourier transform, Journal of Mathematical Analysis and Applications 423 (1), 681-700, 2015. (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
- L Lee, K.I. Kou, W Zhang, J Liang, Y Liu, Robust finite-time boundedness of multi-agent systems subject to parametric uncertainties and disturbances, International Journal of Systems Science, 1-9, 2015 (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
- YH Xia, R Wang, K.I. Kou, D O’Regan, On the linearization theorem for nonautonomous differential equations, Bulletin des Sciences Mathématiques, 2014. (NSFC10901166, MYRG099, MYRG142, FDCT094, FDCT099)
- Y. Yang and K. I. Kou, Uncertainty Principles for Hypercomplex Signals in the Linear Canonical Transform Domains, Signal Processing. Vol. 95, Feb 2014, 67-75. ISSN 0165-1684 [YK13.pdf] (SCIE) (NSFC10901166, MRG002, MYRG099, MYRG142, FDCT094)
- K.I. Kou and J. Morais, Asymptotic Behaviour of the Quaternion Linear Canonical Transform and the Bochner-Minlos Theorem, Applied Mathematics and Computation, 247, 675-688, 2014. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- M. Liu, K.I. Kou, J. Morais and P. Dang, Signal Moments for the Short-Time Fourier Transform Associated with Hardy-Sobolev Derivatives, Mathematical Methods in the Applied Sciences, 2014. (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- J. Morais, K.I. Kou and H.T. Le, Generalized Holomorphic Orthogonal Function Systems over Infinite Cylinders, Mathematical Methods in the Applied Sciences. Article first published online: 12 AUG 2014, DOI: 10.1002/mma.3243 (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- Y. H. Zhang, K.I. Kou and G. T. Deng, Integral Representation and Asymptotic Behavior of Harmonic Functions in Half Space, Journal of Differential Equations, 257(8), 2753-2764 (2014) , DOI: 10.1016/j.jde.2014.05.047 (MRG002, MYRG142, MYRG099, FDCT094, FDCT099, MRG012)
- K. I. Kou, J. Ou^ and J. Morais, On uncertainty principle for quaternionic linear canonical transform, Abstract and Applied Analysis, Vol. 2013, Article ID 725952, 14 pages, (2013). doi:10.1155/2013/725952. [KOM13.pdf] (MYRG142, FDCT094)
- J. Morais, K.I. Kou and W. Sproessig, Generalized holomorphic Szego kernel in 3D spheroids, Computers and Mathematics with Applications, Vol. 65 (4), Feb 2013, 576 – 588, (2013). ISSN: 0898-1221 [MKS13.pdf] (SCIE) (MYRG142, FDCT094)
- J. Morais, K.I. Kou and S. Georgiev, On convergence properties of 3D spheroidal monogenics, International Journal of wavelets multiresolution and information processing, Vol. 11, 1350024, (2013) [19 pages] doi: 10.1142/S0219691313500240, ISSN 0219-6913 [MKG12.pdf] (MYRG142, FDCT094)
- K. Kou, J. Morais and Y. Zhang, Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis, Mathematical Methods in the Applied Sciences, 36: 1028–1041, (2013). doi: 10.1002/mma.2657, ISSN 1073-2772 [KMZ12.pdf] (MYRG142)
- Z. Du, K. Kou and J. Wang^, Lp polyharmonic Dirichlet problems in regular domains I: The unit disc, Complex Variables and Elliptic Equations, Vol. 1, 1-19, (2012). ISSN 1747-6933 (Print), 1747-6941 (Online) [DKW12.pdf] (SCIE) DOI: 10.1080/17476933.2012.678993
- K. Kou, R. Xu^ and Y. Zhang, Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform, Mathematical Methods in the Applied Sciences, 35: 2122–2132. doi: 10.1002/mma.2642 (2012), ISSN 1073-2772 [KXZ11.pdf] (SCIE )
- K. Kou and R. Xu^, Windowed linear canonical transform and its applications, Signal Processing, 92(1), 179-188, (2012). ISSN 0165-1684 [KX12.pdf] (SCI)
- Y. Zhang, G. Deng and K. Kou, On the lower bound for a class of harmonic functions in the half space, Acta Mathematica Scientia, 2012, 32 B (4), 1487-1494. ISSN 0252-9602 [ZDK12.pdf] (SCI)
- Y. Liu^, K. Kou and I. Ho, New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms, Signal Processing, 90(3), 933-945, (2010). ISSN 0165-1684 [LKH10.pdf] (SCI)
- A. Axelsson, K. Kou and T. Qian, Hilbert transforms and the Cauchy integral in Euclidean space, Studia Mathematica, 193(2), 161-187, (2009). [AKQ09.pdf](SCI)
- F. Brackx, N. De Schepper, K. Kou and F. Sommen, The Mehler Formula for the Generalized Clifford-Hermite Polynomials, Acta Mathematica Sinica, English Series, 23(4), 697-704, (2007). ISSN 1439-8516 CN: 11-2039/O1 [FSKS07.pdf](SCI)
- K. Kou , T. Qian and F. Sommen, Sampling with Bessel Functions, Advances in Applied Clifford Albebras, 17(3), 519-536, (2007). ISSN 0188-7009 [KQS07.pdf]
- K. Kou and T. Qian, Shannon Sampling in the Clifford Analysis Setting, Journal for Analysis and its Applications (ZEITSCHRIFT FÜR ANALYSIS UND IHRE ANWENDUNGEN), 24(4), 853-870, (2005). ISSN 0972-5954 [KQ05b.pdf]
- K. Kou and T. Qian, Shannon Sampling and Estimation of Band-limited Functions in the Several Complex Variables Setting, Acta Mathematica Scientia, Series B, English Edition, 25(4), 741-754, Oct (2005). ISSN 0252-9602 CN: 42-1227/0 [KQ05a.pdf]
- K. Kou, T. Qian and F. Sommen, Generalizations of Fueter’s Theorem, Methods and Applications of Analysis, 9(2), 273-290, June (2002). ISSN 1073-2772 [KQS02.pdf]
- K. Kou and T. Qian, The Paley-Wiener Theorem in R^n with the Clifford Analysis Setting, Journal of Funcnctional Analysis, 189(1), 227-241(15), Feb (2002). ISSN 0022-1236 [KQ02.pdf] (SCI)
- K. Kou, V. Sin and X. Jin, A Note on the Fast Algorithm for Block Toeplitz Systems with Tensor Structure, Applied Mathematics and Computation, 126, 187-197 (2002). ISSN 0096-3003 [KSJ02.pdf]
- S. Lei, K. Kou and X. Jin, Circulant-like Block Preconditioners for Ill-Conditioned Block Toeplitz Systems, East-West Journal of Numerical Mathematics, 7(3), 175-185 (1999). ISSN 1513-489X[LKJ99.pdf]
- K. Kou, X. Jin and V. Sin, The Sine Transform Operator in the Banach Space of Symmetric Matrices and Its Application in Image Restoration, Numerical Mathematics, A Journal of Chinese Universities, English series, 8(2), 231-242 (1999). ISSN 1004-8979 [KJS99.pdf]
^ This author is a student under my supervision when he/she completed this article.
Book Chapters
- S. Georgiev, J. Morais, K.I. Kou and W. Sprößig. Bochner-Minlos Theorem and Quaternion Fourier Transform. In Eckhard Hitzer and Steve Sangwine, Quaternion and Clifford Fourier Transforms and Wavelets, Springer, Birkhauser Trends in Mathematics Series, 105-120 (2013). [GMKS13.pdf]
- X. Jin and K. Kou, A Brief Survey of Block Toeplitz Iterative Solvers, Transactions of K. C.Wong Education Foundation Supported Lectures, Vol. 22, pp. 1-27. Ed: W. Qian, Shanghai University Press, 2002.
Refereed Proceeding Papers
- K. Kou, New generalizations of Fueter’s theorem, American Institute of Physics Conference Proceedings, DOI:10.1063/1.3636722 Vol. 1389, pp. 284-287; NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. Date: 19 — 25 September 2011 Location: Halkidiki, (Greece) ISBN: 978-0-7354-0956-9.
- X. Jin and K. Kou, A Brief Survey of Block Toeplitz Iterative Solvers, Transactions of K. C.Wong Education Foundation Supported Lectures, Vol. 22, pp. 1-27. Ed: W. Qian, Shanghai University Press, 2002.
Professional Affiliations
- Founding member of the ISAAC interest group on Clifford and Quaternionic analysis since January, 2011;
- Fellow – Stanley Ho East Asia College (SHEAC), University of Macau.
- Life Member (ID: 4939) of Clare Hall, A College for Advanced Study in the University of Cambridge, United Kingdom.
Contact Details
Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China
Room: E11-3067
Telephone: (853) 8822-4472
Fax: (853) 8822-2426
Email: kikou