✦ LIBER ✦
Fourier type 2 operators with respect to locally compact abelian groups
✍ Scribed by Aicke Hinrichs; Mariusz Piotrowski
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 121 KB
- Volume
- 276
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
A linear and bounded operator T between Banach spaces X and Y has Fourier type 2 with respect to a locally compact abelian group G if there exists a constant c > 0 such that∥T$\hat f$∥~2~ ≤ c∥f∥~2~ holds for all X‐valued functions f ∈ L^X^~2~(G) where $\hat f$ is the Fourier transform of f. We show that any Fourier type 2 operator with respect to the classical groups has Fourier type 2 with respect to any locally compact abelian group. This generalizes previous special results for the Cantor group and for closed subgroups of ℝ^n^. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)