The size of characters of compact Lie groups

• Autorzy: Kathryn E. Hare
• Języki publikacji: EN

Abstrakty

EN

Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then $μ^n ∈ L^1$. When μ is a continuous, orbital measure then $μ^n$ is seen to belong to $L^2$. Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 43A65: Representations of groups, semigroups, etc.
• 22E46: Semisimple Lie groups and their representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 1
• Strony: 1-18

Daty

wydano

1998

otrzymano

1996-03-22

poprawiono

1997-08-11

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1,

Bibliografia

• [1] T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Springer, New York, 1985.
• [2] D. Cartwright and J. McMullen, A structural criterion for the existence of infinite Sidon sets, Pacific J. Math. 96 (1981), 301-317.
• [3] A. Dooley, Norms of characters and lacunarity for compact Lie groups, J. Funct. Anal. 32 (1979), 254-267.
• [4] S. Giulini, P. Soardi and G. Travaglini, Norms of characters and Fourier series on compact Lie groups, ibid. 46 (1982), 88-101.
• [5] K. Hare, Properties and examples of $(L^p,L^q)$ multipliers, Indiana Univ. Math. J. 38 (1989), 211-227.
• [6] K. Hare, Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547-564.
• [7] K. Hare and D. Wilson, A structural criterion for the existence of infinite central Λ (p) sets, Trans. Amer. Math. Soc. 337 (1993), 907-925.
• [8] K. Hare and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95.
• [9] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972.
• [10] J. Lopez and K. Ross, Sidon Sets, Lecture Notes in Pure and Appl. Math. 13, Marcel Dekker, New York, 1975.
• [11] M. Marcus and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Princeton Univ. Press, Princeton, N.J., 1981.
• [12] M. Mimura and H. Toda, Topology of Lie Groups, Transl. Math. Monographs 91, Amer. Math. Soc., Providence, R.I., 1991.
• [13] D. Ragozin, Central measures on compact simple Lie groups, J. Funct. Anal. 10 (1972), 212-229.
• [14] F. Ricci and G. Travaglini, $L^p$-$L^q$ estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras, ibid. 129 (1995), 132-147.
• [15] D. Rider, Central lacunary sets, Monatsh. Math. 76 (1972), 328-338.
• [16] V. Varadarajan, Lie Groups, Lie Algebras and their Representations, Springer, New York, 1984.
• [17] R. Vrem, $L^p$-improving measures on hypergroups, in: Probability Measures on Groups, IX (Oberwolfach, 1988), Lecture Notes in Math. 1379, Springer, Berlin, 1989, 389-397.