Postdoctoral Fellow
Department of Mathematics and Statistics
Room 407, Hamilton Hall
McMaster University,
Hamilton. Ontario, CA. L8S4K1.
Phone:905-525-9140, ext.26079.
Fax:905-522-0935
Email: cklai_at_math.mcmaster.ca
In the coming September 2014, I will be moving to San Francisco State University
Personal
I am now a Postdoctoral Research Fellow in McMaster University under Prof. J-P Gabardo. Before I joined McMaster, I obtained my PhD in Mathematics in the Chinese University of Hong Kong (2012) under the supervision of Prof. Ka-Sing Lau. My thesis title was Spectral Analysis on Fractal Measures and Tiles.
Research Interests
Fourier analysis and harmonic analysis.
Fractal geometry.
Tiling theory.
Frame theory.
More specifically, I study the existence and structure of the exponential orthonormal bases, Fourier frames, Riesz basis, windowed exponentials on fractal measures. Because of its relation with applied harmonic analysis, I am also interested in classical sampling theory and Gabor analysis. And vice versa, I am also interested in applying harmonic analysis techniques to studying fractal geometry.
Publications
You may find my papers on Arxiv.1. On Fourier frame of absolutely continuous measures, J. Funct. Anal., 261 (2011), 2877-2889.
2. (with K.S. Lau and X.G. He), Exponential spectra in L2(\mu), Appl. Comp. Harm. Anal., 34 (2013), 327-338.
3. (with K.S. Lau and H. Rao), Spectral structure of digit sets of self-similar tiles on R^1, Tran. Amer. Math. Soc, 365 (2013), 3831-3850.
4. (with X.G. He and X.R. Dai), Spectral property of Cantor measures with consecutive digits, Adv in Math, 242 (2013), 187-208.
5. (with D. Dutkay) Some reduction of the spectral set conjecture to integers, Math. Cambridge. Proc. Soc., 156 (2014), 123-135.
6. (with D. Dutkay) Uniformity of measures with Fourier frames, Adv in Math., 252 (2014), 684-707.
7. (with J.-P Gabardo) Frames of multi-windowed exponentials on subsets of R^d, To appear in Appl. Comp. Harm. Anal..
8. (with K.S. Lau and H. Rao), Classification of tile digit sets as product-forms, submitted.
9. (with J.-P Gabardo) Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution, submitted.
Teaching
1M03 Calculus for business, Humanities and Social Sciences (Winter 2014), Lecturer.
1ZB3 Engineering Calculus, (Winter 2014), Lecturer.
Stats 1L03 Probability and Linear Algebra (Fall 2013). Lecturer
1K03 (Course Homepage)
1M03 Calculus for business, Humanities and Social Sciences (Winter 2013), Lecturer.
Previous Teaching in The Chinese University of Hong Kong: Teaching assistant of Stochastic Processes, Introductory Probability, Fourier Analysis, Real Analysis.
Useful Links(for research)
Department of Mathematics and Statistics, McMaster University
Department of Mathematics, The Chinese University of Hong Kong
Arxiv search
mathscinet
Other than Math
In my free time, I like to go hiking, cycling and particularly, playing the guitar. I also play bass guitar (it is as exciting as guitar) and jazz drum (just a beginner) in a band. During weekend, I will go to church for worship and service. Here are some good places.
MacNiell Baptist Church (all are welcome)
Joshua Fellowship (every Friday, students are welcome)