**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)