Herz-Schur Multipliers and Non-Uniformly Bounded Representations of Locally Compact Groups

Abstract

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space, such that f is the coefficient of this representation with respect to two vectors with bounded orbit. Moreover, we show that the norm of the representation of an element g from G is at most exponential in terms of the metric distance from g to the identity element of G.

arXiv comment12 pages

References in corpus (2)

• Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces
• Fourier Multiplier Norms of Spherical Functions on the Generalized Lorentz Groups

Cited by in corpus (1)

• Fourier series and twisted C*-crossed products