English

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 L2L^2-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}
}

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24 pages