Uniformly bounded representations for the Lorentz groups

Wilson, Edward N.

doi:10.1090/S0002-9947-1972-0293011-8

Uniformly bounded representations for the Lorentz groups
HTML articles powered by AMS MathViewer

by Edward N. Wilson

Trans. Amer. Math. Soc. 166 (1972), 431-438

DOI: https://doi.org/10.1090/S0002-9947-1972-0293011-8

PDF | Request permission

Abstract:

A family of uniformly bounded class 1 representations of the Lorentz groups is constructed. This family of representations includes, but is larger than, a similar family of representations constructed by Lipsman. The construction technique relies on a multiplicative analysis of various operators under a Mellin transform.

References

Salomon Bochner, Harmonic analysis and the theory of probability, University of California Press, Berkeley-Los Angeles, Calif., 1955. MR 0072370, DOI 10.1525/9780520345294
R. A. Kunze and E. M. Stein, Uniformly bounded representations and harmonic analysis of the $2\times 2$ real unimodular group, Amer. J. Math. 82 (1960), 1–62. MR 163988, DOI 10.2307/2372876
R. A. Kunze and E. M. Stein, Uniformly bounded representations. II. Analytic continuation of the principal series of representations of the $n\times n$ complex unimodular group, Amer. J. Math. 83 (1961), 723–786. MR 163989, DOI 10.2307/2372907
Ronald L. Lipsman, Uniformly bounded representations of the Lorentz groups, Amer. J. Math. 91 (1969), 938–962. MR 267044, DOI 10.2307/2373311

Introduction to the theory of Fourier integrals