Lau, Ka Sing

Chairman & Professor of Mathematics

BSc (CUHK); PhD (Washington)

Email: kslau@math.cuhk.edu.hk
Tel: (+852) 2609 7966
EDUCATION

1969 – 1972 Ph.D. University of Washington (Seattle)
1964 – 1968 B. Sc. The Chinese University of Hong Kong (Magna Cum Laude)
PRESENT POSITION

1996 – Professor of Mathematics & Chairman, CUHK
OTHER PROFESSIONAL EXPERIENCE

1986 – 1999 Professor, University of Pittsburgh
2008 Summer Visiting Professor, Université de Bretagne-Sud
1997 Summer Visiting Professor, Université de Paris-Nord
1995 Winter Visiting Professor, National Sun Yat-Sen University
1994 Summer Visiting Professor, Cornell University
1991 Summer Visiting Professor, Goldsmiths' College, London University
1991 Winter Visiting Professor, Elec. Eng., University of Pittsburgh
1989 Winter Fulbright Fellow, Indian Statistical Inst., New Delhi, India
1982 – 1983 Visiting Member, Institute for Adv. Study, Princeton
1981 Summer Research Fellow, Bulgaria Acad. of Sci., Bulgaria
1980 – 1986 Associate Professor, University of Pittsburgh
1976 – 1977 Exchange Assistant Professor, Kansas State University
1974 – 1980 Assistant Professor, University of Pittsburgh
1972 – 1974 Instructor, University of Chicago
1969 – 1972 Research / teaching assistant, University of Washington
1968 – 1969 Demonstrator, The Chinese University of Hong Kong
PROFESSIONAL OFFICE HOLD

2008 - Associate Editor, Science in China, Mathematics
2005 - Member, UGC Research Grants Council
2004 - Member, Steering Committee and Scientific Committee,
Hang Lung Mathematics Awards
2002 - 2004 President, Hong Kong Mathematics Society
1998 - 2001 Council Member, Hong Kong Institute of Science
1996 - 1998 Associate Director, The Institute of Mathematical Sciences
1996 - Associate Editor, Asian Journal of Mathematics
RESEARCH AREAS

Functional analysis, Harmonic analysis, Fractal geometry, Wavelet theory, Applied probability
PUBLICATIONS (in refereed journals)
  1. Infinite dimensional polytopes, Math. Scand., 32 (1973), 193-213
  2. The dual ball of a Lindenstrauss space, Math. Scand., 33 (1973), 323-337
  3. Extreme opereators on Choquet simplexes, Pacific J. Math., 52 (1974), 129-142
  4. A representation theorem of isometries of C(X,E), Pacific J. Math., 22 (1975), 229-233
  5. Farthest points in weakly compact sets, Israel J. Math., 22 (1975), 168-174
  6. On strongly exposing functionals, J. Aust. Math. Soc., 21 (1976), 362-367
  7. A note on lower semicontinuous set-valued maps, Bull. Pol. Acad. Sci., 4 (1976), 271-273
  8. A remark on strongly exposing functionals, Proc. Amer. Math. Soc., 59 (1976) 242-244
  9. On almost Chebyshev subspaces, J. Approx., Th. 21 (1977), 319-327.
  10. Best approximation by closed sets in Banach spaces, J. Approx., Th. 23 (1978), 29-36.
  11. Differentiability via directional derivatives, Proc. Amer. Math. Soc., 70 (1978), 11-17 (with C. Weil).
  12. Almost Chebyshev subsets in reflexive Banach spaces, Indiana Univ. Math. J., 27 (1978), 791-795.
  13. On a sufficient condition for proximity, Tran. Amer. Math. Soc., 251 (1979), 343-356.
  14. Approximation by continuous vector valued functions, Studia Math., (1980), 291-298.
  15. On generalized harmonic analysis, Tran. Amer. Math. Soc., 259 (1980), 75-97 (with J. Lee).
  16. On the Banach spaces of functions with bounded upper means, Pacific J. Math., 91 (1980), 153-172.
  17. The class of convolution operators on the Marcinkiewicz spaces, Ann. Inst. Fourier, Grenoble 31 (1981), 225-243.
  18. Extension of Wiener's Tauberian identity and multipliers on the Marcinkiewicz Space, Tran. Amer. Math. Soc., 277 (1983), 489-506.
  19. Integrated Cauchy functional equation and characterizations of the exponential law, Sankhya A, 44 (1982), 72-90, (with C.R. Rao).
  20. Solution to the integrated Cauchy functional equation on the whole line, Sankhya A, 46 (1984), 311-318, (with C.R. Rao).
  21. Integrated Cauchy functional equation with an error term and the exponential law, Sankhya A, 46 (1984), 339-354 (with H.M. Gu).
  22. Characterization of the Rao's quadratic entropies, Sankhya A, 47 (1985), 295-309.
  23. On the nonlinear diffusion equation of Kolmogorov, Petrovsky and Piscounov, J. Differential Eq., 59 (1985), 44-70.
  24. Solution of Deny convolution equation restricted to a half line via a random walk approach, J. Multi. Anal., 24 (1988), 309-329 (with A. Alzaid, C.R. Rao and D.N. Shanbhag).
  25. On characteristic functions satisfying a functional equation, and related classes of simultaneous integral equations, Sankhya A, 50 (1988), 190-198 (with B. Ramachandran and H.M. Gu).
  26. Some new classes of Hardy spaces, J. Funct. Anal., 84 (1989), 255-278 (with Y.Z. Chen).
  27. On an equivalent class of norms for BMO, J. Aust. Math. Soc., 46 (1989), 289-295 (with Y.Z. Chen).
  28. Wiener transformation on functions with bounded averages, Proc. Amer. Math. Soc., 108, (1990), 411-421 (with Y.Z. Chen).
  29. On the geometry of spheres in normed linear spaces, J. Aust. Math. Soc., 48 (1990), 101-112 (with J. Gao).
  30. Characterization of the exponential distribution by the relevation transform, J. Applied Prob., 27 (1990), 726-729 (with B.L.S. Prakasa Rao).
  31. On the convolution equation of Choquet and Deny on semigroups, Studia Math., 97 (1990), 115-135 (with W. Zeng).
  32. The sum of Rademacher functions and Hausdorff dimension, Math. Proc. Camb. Phil. Soc., 108 (1990), 97-103 (with T.Y. Hu).
  33. On two classes of Banach spaces with uniform normal structure, Studia Math., 99 (1991), 41-56 (with J. Gao).
  34. Fractal measures and mean p-variations, J. Funct. Anal., 108 (1992), 427-457.
  35. Fractal dimensions and singularities of the Weierstrass type functions, Tran. Amer. Math. Soc., 335 (1993), 649-665, (with T.Y. Hu).
  36. Mean quadratic variations and Fourier asymptotics of self-similar measures, Monatshefte Math., 115 (1993), 99-132, (with J. Wang).
  37. Dimension of a family of singular Bernoulli convolutions, J. Funct. Anal., 116 (1993), 335-358.
  38. Hausdorff dimension of the level sets of Rademacher series, Bull. Polish Acad. Sci., 41 (1993), 11-18 (with T.Y. Hu).
  39. On the Hausdorff dimension of the graph of the perturbed Rademacher series, Real Anal. Exchange, 19 (1994), 457-464, (with T.Y. Hu).
  40. Solutions of the operator-valued integrated Cauchy functional equation, J. Operator Theory, 32 (1994), 157-183 (with C.H. Chu).
  41. Characterization of Lp-solutions for the two-scale dilation equations, SIAM J. Math. Anal., 26 (1995), 1018-1046 (with J. Wang).
  42. Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures, Studia Math., 117 (1995), 1-28, (with J. Wang and C.H. Chu).
  43. On some sharp regularity estimations of L2-scaling functions, SIAM J. Math. Anal., 27 (1996), 835-864, (with M. Ma and J. Wang).
  44. A weighted Tauberian theorem, J. Fourier Anal. and Appl., 2 (1996), 397-406.
  45. On the discount sum of Bernoulli random variables, J. of Stat. Planning and Inference, 63 (1997), 231-246 (with A. Ho).
  46. The regularity of Lp-scaling functions, Asian J. Math., (1997), 272-292 (with M.F. Ma).
  47. Asymptotic behavior of multiperiodic functions, J. Fourier Anal. and Appl., 4 (1998), 129-150 (with A. Fan).
  48. Lq-spectrum of the Bernoulli convolution associated with the golden ratio, Studia Math., 131 (1998), 225-251 (with S.M. Ngai).
  49. Embedding locally compact semigroups into groups, Semigroup Forum, 56 (1998), 151-156 (with J. Lawton, W.B. Zeng).
  50. Multifractal measures and a weak separation condition, Advances in Math., 141 (1999), 45-96 (with S.M. Ngai).
  51. Iterated function system and Ruelle operator, J. Math. Anal. Appl., 231 (1999), 319-344 (with A. Fan).
  52. Asymptotic regularity of Daubechies scaling functions, Proc. AMS, 128 (1999), 1087-1095 (with Q. Sun).
  53. Lq-spectrum of Bernoulli convolutions associated with P.V. numbers, Osaka J. Math., 36 (4) (1999), 993-1010 (with S.M. Ngai).
  54. On the boundary of attractors with non-void interior, Proc. AMS, 128 (1999), 1761-1768 (with Y. Xu).
  55. On the connectedness of self-affine tiles, J. London Math. Soc., (2) 62 (2000), 291-304 (with I. Kirat).
  56. Iterated function systems with overlaps, Asian J. Math., 4 (2000), 527-552 (with A. Fan and S.M. Ngai).
  57. Second order self-similar identities and multifractal decompositions, Indiana U. Math. J., 49 (2000), 925-972 (with S.M. Ngai).
  58. Iterated function systems with overlaps and self-similar measures, J. London Math. Soc., 63 (2001), 99-116 (with S.M. Ngai and H. Rao).
  59. Lp-solution of refinement equations, J. Fourier Anal. and Appl., 7 (2001), 143-167 (with R. Jia and D.X. Zhou).
  60. Multifractal structure of the convolution of Cantor measure, Adv. in Appl. Math., 27 (2001), 1-16 (with T. Hu).
  61. Measure representation and multifractal analysis of complete genomes, Phy. Rev. E, 64, (2001), 031903-1 to 031903-9 (with Z. Yu and V. Anh).
  62. Ruelle operator with nonexpansive IFS, Studia Math., 148 (2001), 143--169 (with Y.L. Ye).
  63. Corrigendum to: iterated function system and Ruelle operator, J. Math. Anal. Appl., 262 (2001), 446-451 (with H. Rao and Y. Ye).
  64. Multifractal characterization of complete genomes, Journal of Physics A: Mathematical and General, 34 (2001), 7127-7139 (with Vo Anh and Zu-Guo Yu).
  65. Multifractal characterisation of length sequences of coding and noncoding segments in a complete genome, Physica A, 301 (2001) 351-361 (with Zu-Guo Yu and Vo Anh).
  66. On the absolute continuity of a class of invariant measures, Proc AMS, 130 (2001), 759-767 (with T.Y. Hu and X.Y. Wang).
  67. Relationships between different dimensions of a measure, Monatshefte Math., 135 (2002), 191-201 (with A.H. Fan and H. Rao).
  68. Classification of integral expanding matrices and self-affine tiles, Discrete and Comp. Geometry, 28 (2002), 49-73 (with I. Kirat).
  69. The pressure function for products of non-negative matrices, Math. Research Letters, 9 (2002), 363-378 (with D.J. Feng).
  70. Hausdorff dimension of random fractals with overlaps, Bull. Aust. Math. Soc., 65 (2002), 315-328. (with Z.G. Yu and V.V. ANH)
  71. Fourier asymptotics of Cantor type measures at infinity, Proc AMS, 130 (2002), 2711-2717 (with T.Y. Hu).
  72. Ergodic limits on the conformal repellers, Advances in Math., 169 (2002), 58-91 (with D. Feng and J. Wu).
  73. Recognition of an organism from fragments of its complete genome, Phy. Rev. E., 66 (2002), 031910, 1-9 (with V. Anh and Z.G. Yu).
  74. On one-dimensional self-similar tilings and pq-tiles, Tran AMS, 355 (2002), 1401-1414 (with H. Rao).
  75. Self-affine sets and graph-directed systems, Constr. Appr., 19 (2003), 373-397 (with X.G. He and H. Rao).
  76. Cauchy-transforms of self-similar measures: The Laurent coefficients, J. Functional Anal., 202 (2003), 67-97 (with X.H. Dong).
  77. Heat kernels on metric measure spaces and an application to semilinear elliptic equations, Tran. AMS, 355 (2003), 2065-2093 (with A. Grigoryan and J. Hu).
  78. Dimensions of the boundaries of self-similar sets, Experimental Math., 12 (2003), 13-26 (with S. Ngai).
  79. The genomic tree of living organisms based on a fractal model, Physics Letters A, 317 (2003), 293-302 (with Zu-Guo Yu, V. Anh and K.H. Chu).
  80. Multifractal and correlation analysis of protein sequences from complete genome, Phy. Rev. E., 68 (2003), 021903, 1-10 (with Z.G. Yu and V. Anh).
  81. Iterated function system and multifractal analysis of biological sequences, International Journal of Modern Physics B, 17 (2003), 4367-4375 (with Z.G. Yu and V. Anh).
  82. Expanding polynomials and connectedness of self-affine tiles, Discrete & Comp. Geom., 31 (2004), 275-286 (with I. Kirat and H. Rao).
  83. Iterated function systems with a weak separation condition, Studia Math., 161 (2004), 249-268 (with X.Y. Wang).
  84. Characterization of tile digit sets with prime determinants, Applied and Computational Harmonic Analysis, 16 (2004), 159-173 (with X.G. He).
  85. Fractal analysis of measure representation of large proteins based on the detailed HP model, Phy., 337 (2004), 171-184 (with Z.G. Yu and V. Anh).
  86. Chaos game representation of protein sequences based on the detailed HP model and their multifractal and correlation analysis, J. Th. Biology, 226 (2004), 341-348 (with Z.G. Yu and V. Anh).
  87. An integral related to the Cauchy transform on the Sierpinski gasket, Experimental Math, 13 (2004), 415-419 (with X.H. Dong).
  88. Wavelet decomposition of Calderón-Zygmund operators on function spaces, J. Aust. Math. Soc., 77 (2004), 29-46 (with L. Yan).
  89. Some exceptional phenomena in multifractal formalism: Part I, Asian J. Math., 9 (2005), 275-294 (with X.Y. Wang).
  90. Some exceptional phenomena in multifractal formalism: Part II, Asian J. Math., 9 (2005), 473-488 (with D.J. Feng and X.Y. Wang).
  91. Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces, J. Functional Anal., 237 (2006), 427-445 (with A. Grigoryan and J.X. Hu).
  92. Laplace operators related to self-similar measures on Rd, J. Functional Anal., 239 (2006), 542-565 (with J.X. Hu and S.M. Ngai).
  93. A generalized finite type condition for iterated function systems, Adv. Math., 208 (2007), 647-671 (with S.M. Ngai).
  94. Disklikeness of planar self-affine tiles, Tran Amer. Math. Soc., 359 (2007), No. 7, 3337-3355 (with K.S. Leung).
  95. Obtaining upper bounds of heat kernels from lower bounds, Comm. on Pure and Appl. Math., 61 (2008), 639-660 (with A. Grigoryan and J.X. Hu).
  96. On a generalized dimension of self-affine fractals, Math. Nachr., 281 (2008), 1142-1158 (with X.G. He).
  97. Open set condition and post-critically finite self-similar sets, Nonlinearity, 21 (2008), 1227-1232 (with Q. Deng).
  98. Spectral property of the Bernoulli convolutions, Adv. Math., 219 (2008), 554-567 (with T.Y. Hu).
  99. Self-affine measures and vector-valued representations, Studia Math., 188 (2008), 259-286 (with Q. Deng & X.G. He).
  100. The spectrum of Poincaré recurrence, Ergod. Th. & Dyn. Sys. 28 (2008), 1917-1943 (with L. Shu).
  101. Separation conditions for conformal iterated function systems, Monatsh. Math., 156 (2009), 325-355, (with S.M. Ngai and X.Y. Wang).
  102. Self-similar sets as hyperbolic boundaries, Indiana U. Math. J., 58 (2009), 1777-1795 (with X.Y. Wang).
  103. Multifractal formalism for self-similar measures with weak separation condition, J. Math. Pures Appl., 92 (2009), 407-428 (with D.J. Feng).
  104. Comparison inequalities for heat semigroups and heat kernels on metric measure spaces, J. Funct. Anal., 259 (2010) 2613-2641 (with A. Grigoryan and J.X.Hu).
  105. On the Weyl-Heisenberg frames generated by simple functions, J. Funct. Anal., 261 (2011), 1010-1027 (with X.G. He).
  106. Connectedness of a class of planar self-affine tiles, J. Math. Anal. Appl., 380 (2011), 493-500 (with Q.R. Deng).
  107. Post-critically finite fractals and Martin boundary, Tran. AMS (to appear) (with H. Ju and X.Y. Wang)
  108. Height reducinig property of polynomials and self-affine tiles, Geom. Dedi-cate, to appear (with X.G. He and I. Kirat).
PUBLICATIONS (in refereed conference proceedings)
  1. On some classes of Banach spaces and generalized harmonic analysis, Contemporary Math., 2 (1980), 213-226.
  2. Harmonic analysis on functions with bounded means, 1987 summer conference on harmonic analysis, Contemporary Math., 91 (1989), 165-175 (with Y.Z. Chen).
  3. On a convolution equation and its applications to characterization problems, Proc. Bose Symp. on Prob. Stat. and Design of Experiment, Wiley Eastern, (1990), 75-85 (with B. Zeng).
  4. Integrated Cauchy functional equation with an error term on [0,∞), Proc. Bose conf. on Prob. Stat. and Design of Experiment, Wiley Eastern (1990), (with B. Ramachandran).
  5. On the Lp-Lipschitz exponents of the scaling functions, Proceeding conference on spline functions and wavelets, CRM Proceedings and Lecture Notes, 18 (1999), 181-192 (with M.F. Ma).
  6. On the connectedness and classification of self-affine tiles, International Conference on Wavelet Analysis and its Applications, AMS/IP Studies in Adv. Math., 25 (2002), 193-206.
  7. On the self-affine sets and scaling functions, Wavelet Analysis twenty years of developments, ed. D.X. Zhou, World Scientific (2002), 179-195 (with X.G. He and H. Rao).
  8. Differentiability of pressure functions for product of non-negative matrices, Complex Dym. and Related Topics, ed. by Y. Jiang and Y.F. Wang (2004), 129-146 (with D.J. Feng).
  9. On Some problems of self-affine tiles, Proceeding of ICCM 2001, (2004) 483-493, International Press (with I. Kirat and H. Rao).
  10. Cantor boundary behavior and Cauchy transform on the Sierpinski gasket, Proceedings of ICCM 2007, Vol. I 549-562, International Press (with X.H. Dong).
  11. Cantor boundary behavior of analytic functions, Proceeding on Fractals and Related Fields (to appear), (with X.H. Dong).
SPECIAL INVITED SURVEY ARTICLES
  1. Self-similarity, Lp-spectrum and multifractal formalism, Progress in Prob., 37 (1995), 55-90.
  2. Iterated function systems with overlaps and multifractal structure, Trends in prob. and related analysis, World Scientific, (1998), 35-76.
  3. Multifractal structure and product of matrices, Analysis Th. and Appl., 19:4 (2003), 289-311.
  4. Heat kernel on metric measure spaces with doubling measure, Progress in Prob., 61 (2009), 3-44.
PAPER IN BOOK CHAPTER

Comments on “Harmonic analysis and group theory'”, Nobert Weiner: Collected work Vol. II, Edited by P. Masani (1980).
MONOGRAPH

Functional equations in probability theory, Academic Press (1991) (with B. Ramachandran)
CONFERENCE PROCEEDINGS (Editor)
  1. Advances in Wavelets, Springer Verlag, (1999).
  2. The Third International Congress of Chinese Mathematicians Vol. I and II, Studies in Advanced Mathematics, American Mathematical Society, International Press (2008) (with S.T. Yau and Z.P. Xin).

Return to The Department of Mathematics, The Chinese University of Hong Kong