Titchmarsh theorems for Fourier transforms of H\"older-Lipschitz functions on compact homogeneous manifolds
Functional Analysis
2017-02-21 v1 Classical Analysis and ODEs
Representation Theory
Abstract
In this paper we extend classical Titchmarsh theorems on the Fourier transform of H\"older-Lipschitz functions to the setting of compact homogeneous manifolds. As an application, we derive a Fourier multiplier theorem for -H\"older-Lipschitz spaces on compact Lie groups. We also derive conditions and a characterisation for Dini-Lipschitz classes on compact homogeneous manifolds in terms of the behaviour of their Fourier coefficients.
Keywords
Cite
@article{arxiv.1702.05731,
title = {Titchmarsh theorems for Fourier transforms of H\"older-Lipschitz functions on compact homogeneous manifolds},
author = {Radouan Daher and Julio Delgado and Michael Ruzhansky},
journal= {arXiv preprint arXiv:1702.05731},
year = {2017}
}
Comments
24 pages