Analytic uniformly bounded representations of

Author:
Ronald J. Stanke

Journal:
Trans. Amer. Math. Soc. **290** (1985), 281-302

MSC:
Primary 22E46; Secondary 22E30

MathSciNet review:
787966

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Abstract: By analytically continuing suitably normalized spherical principal series, a family of uniformly bounded representations of , all of which act on the same Hilbert space , is constructed which is parametrized by complex numbers lying in the strip . The proper normalization of the principal series representations involves the intertwining operators of equivalent principal series representations. These intertwining operators are first analyzed using Fourier analysis on the Heisenberg group.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1985-0787966-1

Keywords:
Fourier analysis on the Heisenberg group,
homogeneous norms,
spherical principal series,
intertwining operators,
Laguerre polynomials,
gamma function,
analytic continuation of operators,
uniformly bounded representations

Article copyright:
© Copyright 1985
American Mathematical Society