# About Chun Kit Lai

## At SF State Since:

## Bio:

Click Here for detailed webpage.

**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 in refereed journals

*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, Appl. Comp. Harm. Anal., 36 (2014), 461-472.

8. (with J.-P Gabardo) Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution, J. Fourier. Anal. Appl., 20 (2014), 453-475.

9. (with J.-P Gabardo and Y. Wang), Gabor orthonormal bases generated by the unit cubes, J. Funct. Anal., 269 (2015), 1515-1538.

10. (with Y. Wang), Non-spectral fractal measures with Fourier frames, To appear in J. Fractal Geometry.

11. (with D. Dutkay), Spectral measures generated by arbitrary and random convolution, To appear in J. Math Pure. Appl. .

12. (with K.S. Lau and H. Rao), Classification of tile digit sets as product-forms, To appear in Tran. Amer. Math. Soc.

13. (with D. Dutkay) Self-affine spectral measures and frame spectral measures on R^d, submitted.

14. (with D. Dutkay and J. Hausserman) Hadamard triples generate self-affine spectral measures, submitted.

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#### Publications in Conference Proceedings

1. (with X.-R. Dai, X.-G. He) Law of pure types and some exotic spectra of fractal spectral measures, Proceeding in Mathematics and Statistics 88, pp 47–64, Geometry and Analysis of Fractals, D.-J. Feng and K. S. Lau (eds.), Springer, 2014.

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#### Teaching

Graduate Course taught at San Francisco State University:

*Fall 2016*: MATH 710 Graduate Analysis

*Spring 2016:* MATH 890: **Frame theory and Compressed sensing. **Lectures are provided. Comments welcome

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6

Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12

Undergraduate Courses taught at San Francisco State University

MATH 226: Calculus (I)

MATH 227: Calculus(II)

MATH 228: Calculus (III)

MATH 325: Linear algebra

MATH 380: Complex Variable

MiniCourse in The Chinese University of Hong Kong (2013): Fractal Sets and their Analysis.

Previous teaching in McMaster University: Calculus for business (I) and (II), Engineering Calculus (II), Probability and Linear Algebra.

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