# Classical Harmonic Analysis and Locally Compact Groups

@inproceedings{Reiter1968ClassicalHA, title={Classical Harmonic Analysis and Locally Compact Groups}, author={Hans Reiter}, year={1968} }

1. Classical harmonic analysis and Wiener's theorem 2. Function algebras and the generalization of Wiener's theorem 3. Locally compact groups and the Haar measure 4. Locally compact abelian groups and the foundations of harmonic analysis 5. Functions on locally compact abelian groups 6. Wiener's theorem and locally compact abelian groups 7. The spectrum and its applications 8. Functions on general locally compact groups A. Additional material B. Notes and additional references . References…

## 826 Citations

### Frame theory for locally compact abelian groups

- MathematicsOptics & Photonics - Optical Engineering + Applications
- 2013

Analysis on locally compact abelian groups and local fields has applications in a variety of different fields. Traditional Fourier analysis is based on the characters of Rn, Tn, and Zn. There is a…

### Admissible Wavelets on Groups and their Homogeneous Spaces

- Mathematics
- 2014

In this note, let G be a locally compact group and H be a compact subgroup of G. We investigate the square integrable representations of homogeneous spaces G/H and admissible wavelets for these…

### Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups

- Mathematics
- 2003

In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian…

### Quasi-Banach modulation spaces and localization operators on locally compact abelian groups

- MathematicsBanach Journal of Mathematical Analysis
- 2022

We introduce new quasi-Banach modulation spaces on locally compact abelian groups which coincide with the classical ones in the Banach setting and prove their main properties. Then, we study Gabor…

### On the Fourier transform on function algebras on locally compact Abelian groups

- Mathematics
- 2017

We obtain a characterisation of the Fourier transform on the space of Schwartz–Bruhat functions and the Feichtinger algebra on locally compact Abelian groups. The result states that any appropriately…

### Weighted $L^p-$spaces on nilpotent, locally compact groups

- Mathematics
- 2017

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an…

### A converse of Bernstein's inequality for locally compact groups

- MathematicsBulletin of the Australian Mathematical Society
- 1973

Let G be a Hausdorff locally compact abelian group, Γ its character group. We shall prove that, if S is a translation-invariant subspace of Lp (G) (p ∈ [1, ∞]), for each a ∈ G and , then is…

### On an isomorphism theorem for the Feichtinger's Segal algebra on locally compact groups

- Mathematics
- 2021

In this article we observe that a locally compact group G is completely determined by the algebraic properties of its Feichtinger’s Segal algebra S0(G). Let G and H be locally compact groups. Then…

### Harmonic Analysis of Generalized Stochastic Processes on Locally Compact Abelian Groups

- Mathematics
- 2003

Introduction Whereas ordinary functions on a locally compact group map the group elements into the complex numbers, a stochastic process can be understood as a mapping into a Hilbert space. The idea…