Titchmarsh theorems on Damek-Ricci spaces via moduli of continuity of higher order

2022/05/12 by Manoj Kumar, Vishvesh Kumar, Kumar, Manoj +3
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2205.06028

openalex publication_date 2022/05/12 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

A classical theorem of Titchmarsh relates the L²-Lipschitz functions and decay of the Fourier transform of the functions. In this note, we prove the Titchmarsh theorem for Damek-Ricci space (also known as harmonic NA groups) via moduli of continuity of higher orders. We also prove an analogue of another Titchmarsh theorem which provides integrability properties of the Fourier transform for functions in the Hölder Lipschitz spaces.

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