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1

Obtaining upper bounds of heat kernels from lower bounds

Alexander Grigor′yan, Jiaxin Hu, Ka-Sing Lau

Journal:

Communications on Pure and Applied Mathematics

Year:

2008

Language:

english

File:

PDF, 188 KB

english, 2008

2

Heat Kernels on Metric Measure Spaces and an Application to Semilinear Elliptic Equations

Alexander Grigor'Yan, Jiaxin Hu and Ka-Sing Lau

Journal:

Transactions of the American Mathematical Society

Year:

2003

Language:

english

File:

PDF, 2.43 MB

english, 2003

3

A Counterexample to the “Hot Spots” Conjecture on Nested Fractals

Lau, Ka-Sing, Li, Xiao-Hui, Ruan, Huo-Jun

Journal:

Journal of Fourier Analysis and Applications

Year:

2017

Language:

english

File:

PDF, 1.01 MB

english, 2017

4

A generalized finite type condition for iterated function systems

Ka-Sing Lau, Sze-Man Ngai

Journal:

Advances in Mathematics

Year:

2007

Language:

english

File:

PDF, 261 KB

english, 2007

5

Spectral property of the Bernoulli convolutions

Tian-You Hu, Ka-Sing Lau

Journal:

Advances in Mathematics

Year:

2008

Language:

english

File:

PDF, 160 KB

english, 2008

6

Cauchy transforms of self-similar measures: the Laurent coefficients

Xin-Han Dong, Ka-Sing Lau

Journal:

Journal of Functional Analysis

Year:

2003

Language:

english

File:

PDF, 311 KB

english, 2003

7

Post-critically finite fractal and Martin boundary

Ju, Hongbing, Lau, Ka-Sing, Wang, Xiang-Yang

Journal:

Transactions of the American Mathematical Society

Year:

2012

Language:

english

File:

PDF, 267 KB

english, 2012

8

Fractal Dimensions and Singularities of the Weierstrass Type Functions

Tian-You Hu and Ka-Sing Lau

Journal:

Transactions of the American Mathematical Society

Year:

1993

Language:

english

File:

PDF, 1.43 MB

english, 1993

9

Cauchy transforms of self-similar measures: Starlikeness and univalence

Dong, Xin-Han, Lau, Ka-Sing, Wu, Hai-Hua

Journal:

Transactions of the American Mathematical Society

Year:

2016

Language:

english

File:

PDF, 1.55 MB

english, 2016

10

On hyperbolic graphs induced by iterated function systems

Lau, Ka-Sing, Wang, Xiang-Yang

Journal:

Advances in Mathematics

Year:

2017

Language:

english

File:

PDF, 511 KB

english, 2017

11

Multifractal Measures and a Weak Separation Condition

Ka-Sing Lau, Sze-Man Ngai

Journal:

Advances in Mathematics

Year:

1999

Language:

english

File:

PDF, 442 KB

english, 1999

12

Ergodic Limits on the Conformal Repellers

De-Jun Feng, Ka-Sing Lau, Jun Wu

Journal:

Advances in Mathematics

Year:

2002

Language:

english

File:

PDF, 284 KB

english, 2002

13

Iterated Function System and Ruelle Operator

Ai Hua Fan, Ka-Sing Lau

Journal:

Journal of Mathematical Analysis and Applications

Year:

1999

Language:

english

File:

PDF, 177 KB

english, 1999

14

Some new classes of Hardy spaces

Yong-Zhuo Chen, Ka-Sing Lau

Journal:

Journal of Functional Analysis

Year:

1989

Language:

english

File:

PDF, 898 KB

english, 1989

15

Fractal measures and mean p-variations

Journal:

Journal of Functional Analysis

Year:

1992

Language:

english

File:

PDF, 1.24 MB

english, 1992

16

Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces

Alexander Grigor'yan, Jiaxin Hu, Ka-Sing Lau

Journal:

Journal of Functional Analysis

Year:

2006

Language:

english

File:

PDF, 167 KB

english, 2006

17

Laplace operators related to self-similar measures on

Jiaxin Hu, Ka-Sing Lau, Sze-Man Ngai

Journal:

Journal of Functional Analysis

Year:

2006

Language:

english

File:

PDF, 229 KB

english, 2006

18

On the Weyl–Heisenberg frames generated by simple functions

Xing-Gang He, Ka-Sing Lau

Journal:

Journal of Functional Analysis

Year:

2011

Language:

english

File:

PDF, 178 KB

english, 2011

19

Embedding Locally Compact Semigroups into Groups

Ka-Sing Lau, Jimmie Lawson, Wei-Bin Zeng

Journal:

Semigroup Forum

Year:

1998

Language:

english

File:

PDF, 69 KB

english, 1998

20

Separation conditions for conformal iterated function systems

Ka-Sing Lau, Sze-Man Ngai, Xiang-Yang Wang

Journal:

Monatshefte für Mathematik

Year:

2009

Language:

english

File:

PDF, 364 KB

english, 2009

21

Relationships between Different Dimensions of a Measure

Ai-Hua Fan, Ka-Sing Lau, Hui Rao

Journal:

Monatshefte für Mathematik

Year:

2002

Language:

english

File:

PDF, 96 KB

english, 2002

22

Farthest points in weakly compact sets

Journal:

Israel Journal of Mathematics

Year:

1975

Language:

english

File:

PDF, 244 KB

english, 1975

23

Lipschitz equivalence of self-similar sets and hyperbolic boundaries

Luo, Jun Jason, Lau, Ka-Sing

Journal:

Advances in Mathematics

Year:

2013

Language:

english

File:

PDF, 2.82 MB

english, 2013

24

Cantor boundary behavior of analytic functions

Xin-Han Dong, Ka-Sing Lau, Jing-Cheng Liu

Journal:

Advances in Mathematics

Year:

2013

Language:

english

File:

PDF, 754 KB

english, 2013

25

On Generalized Harmonic Analysis

Ka-Sing Lau and Jonathan K. Lee

Journal:

Transactions of the American Mathematical Society

Year:

1980

Language:

english

File:

PDF, 1.62 MB

english, 1980

26

On spectral N-Bernoulli measures

Dai, Xin-Rong, He, Xing-Gang, Lau, Ka-Sing

Journal:

Advances in Mathematics

Year:

2014

Language:

english

File:

PDF, 370 KB

english, 2014

27

Estimates of heat kernels for non-local regular Dirichlet forms

Grigor’yan, Alexander, Hu, Jiaxin, Lau, Ka-Sing

Journal:

Transactions of the American Mathematical Society

Year:

2014

Language:

english

File:

PDF, 511 KB

english, 2014

28

On the equivalence of homogeneous iterated function systems

Deng, Qi-Rong, Lau, Ka-Sing

Journal:

Year:

2013

Language:

english

File:

PDF, 151 KB

english, 2013

29

Spectral structure of digit sets of self-similar tiles on ${\mathbb R}^1$

Lai, Chun-Kit, Lau, Ka-Sing, Rao, Hui

Journal:

Transactions of the American Mathematical Society

Year:

2013

Language:

english

File:

PDF, 327 KB

english, 2013

30

Spectrality of a class of infinite convolutions

An, Li-Xiang, He, Xing-Gang, Lau, Ka-Sing

Journal:

Advances in Mathematics

Year:

2015

Language:

english

File:

PDF, 389 KB

english, 2015

31

Differentiability Via Directional Derivatives

Ka-Sing Lau and Clifford E. Weil

Journal:

Proceedings of the American Mathematical Society

Year:

1978

Language:

english

File:

PDF, 211 KB

english, 1978

32

Wiener Transformation on Functions with Bounded Averages

Yong-Zhuo Chen and Ka-Sing Lau

Journal:

Proceedings of the American Mathematical Society

Year:

1990

Language:

english

File:

PDF, 257 KB

english, 1990

33

Sierpinski-type spectral self-similar measures

Deng, Qi-Rong, Lau, Ka-Sing

Journal:

Journal of Functional Analysis

Year:

2015

Language:

english

File:

PDF, 400 KB

english, 2015

34

Disklikeness of Planar Self-Affine Tiles

King-Shun Leung and Ka-Sing Lau

Journal:

Transactions of the American Mathematical Society

Year:

2007

Language:

english

File:

PDF, 1.63 MB

english, 2007

35

Extension of Wiener's Tauberian Identity and Multipliers on the Marcinkiewicz Space

Journal:

Transactions of the American Mathematical Society

Year:

1983

Language:

english

File:

PDF, 1.53 MB

english, 1983

36

On a Sufficient Condition for Proximity

Journal:

Transactions of the American Mathematical Society

Year:

1979

Language:

english

File:

PDF, 396 KB

english, 1979

37

On One-Dimensional Self-Similar Tilings and pq-Tiles

Ka-Sing Lau and Hui Rao

Journal:

Transactions of the American Mathematical Society

Year:

2003

Language:

english

File:

PDF, 1.33 MB

english, 2003

38

Insomnia and health-related quality of life in stroke

Tang, Wai-Kwong, Grace Lau, Chieh, Mok, Vincent, Ungvari, Gabor S, Wong, Ka-Sing

Journal:

Topics in Stroke Rehabilitation

Year:

2015

Language:

english

File:

PDF, 148 KB

english, 2015

39

Characterization of Rao's Quadratic Entropies

Journal:

Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)

Year:

1985

Language:

english

File:

PDF, 1.16 MB

english, 1985

40

Wiener transformation on functions with bounded averages

Chen, Yong Zhuo, Lau, Ka-Sing

Journal:

Proceedings of the American Mathematical Society

Year:

1990

Language:

english

File:

PDF, 660 KB

english, 1990

41

Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces

GRIGOR'YAN, Alexander, HU, Jiaxin, LAU, Ka-Sing

Journal:

Journal of the Mathematical Society of Japan

Year:

2015

Language:

english

File:

PDF, 716 KB

english, 2015

42

Random walks and induced Dirichlet forms on self-similar sets

Kong, Shi-Lei, Lau, Ka-Sing, Wong, Ting-Kam Leonard

Journal:

Advances in Mathematics

Year:

2017

Language:

english

File:

PDF, 665 KB

english, 2017

43

Characterization of a class of planar self-affine tile digit sets

An, Li-Xiang, Lau, Ka-Sing

Journal:

Transactions of the American Mathematical Society

Year:

2019

Language:

english

File:

PDF, 371 KB

english, 2019

44

Fractal dimensions and singularities of the Weierstrass type functions

Hu, Tian You, Lau, Ka-Sing

Journal:

Transactions of the American Mathematical Society

Year:

1993

Language:

english

File:

PDF, 1.36 MB

english, 1993

45

On a generalized dimension of self-affine fractals

Xing-Gang He, Ka-Sing Lau

Journal:

Mathematische Nachrichten

Year:

2008

Language:

english

File:

PDF, 617 KB

english, 2008

46

Multifractal Structure of Convolution of the Cantor Measure

Tian-You Hu, Ka-Sing Lau

Journal:

Advances in Applied Mathematics

Year:

2001

Language:

english

File:

PDF, 138 KB

english, 2001

47

Volume 231, Number 2 (1999), in the article “Iterated Function System and Ruelle Operator,” by Ai Hua Fan and Ka-Sing Lau, pages 319–344 ():

Ka-Sing Lau, Hui Rao, Yuan-Ling Ye

Journal:

Journal of Mathematical Analysis and Applications

Year:

2001

Language:

english

File:

PDF, 69 KB

english, 2001

48

On almost Chebyshev subspaces

Journal:

Journal of Approximation Theory

Year:

1977

Language:

english

File:

PDF, 462 KB

english, 1977

49

Best approximation by closed sets in Banach spaces

Journal:

Journal of Approximation Theory

Year:

1978

Language:

english

File:

PDF, 353 KB

english, 1978

50

On the nonlinear diffusion equation of Kolmogorov, Petrovsky, and Piscounov

Journal:

Journal of Differential Equations

Year:

1985

Language:

english

File:

PDF, 978 KB

english, 1985