Titchmarsh theorems on Damek–Ricci spaces via moduli of continuity of higher order
A classical theorem of Titchmarsh relates the [Formula: see text]-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 [Formula: see text] 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.
Authors
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Vishvesh Kumar (ORCID: https://orcid.org/0000-0003-4799-9029)
- Manoj Kumar (ORCID: https://orcid.org/0000-0001-7209-1886)
Institutions
- Queen Mary University of London (GB)
- Center for Discrete Mathematics and Theoretical Computer Science (US)
- Indian Institute of Science Bangalore (IN)
Publication Details
- Journal
- International Journal of Mathematics
- Published
- 2024-12-07
- DOI
- https://doi.org/10.1142/s0129167x25500016
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fonds Wetenschappelijk Onderzoek
- Universiteit Gent
- National Board for Higher Mathematics
- Engineering and Physical Sciences Research Council
- Bijzonder Onderzoeksfonds UGent