# Abstract Harmonic Analysis

@inproceedings{Hewitt1963AbstractHA, title={Abstract Harmonic Analysis}, author={Edwin Shields Hewitt and Kenneth A. Ross}, year={1963} }

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#### 3,587 Citations

THE PARSEVAL FORMULA IN THE HARMONIC ANALYSIS FOR OPERATOR AND THE SUPPORT FOR OPERATORS

- Mathematics
- 1988

Abstract In this paper a harmonic analysis for operators on a homogeneous Banach space on the additional group of real numbers is discussed. Main results are as following:
1. The Parseval formula… Expand

Classical Themes of Fourier Analysis

- Mathematics
- 1991

This article is devoted to “Harmonic Analysis for itself” (a quotation from the preceding article), more precisely, to specific problems of the classical theory of Fourier series (and, to a certain… Expand

Operator theory in harmonic analysis

- Mathematics
- 1977

The purpose of this paper is to give an illustration of how operator theoretic results in Hilbert space can be applied to obtain results in classical and abstract harmonic analysis. An inequality for… Expand

Harmonic Analysis and Functional Equations

- Physics
- 1998

Functional equations occur in many parts of mathematics, also in harmonic analysis. As an example we mention that the complex exponential function 7 :x ? exp (?x) for any ? ∈ R is a solution of… Expand

Projections in $L^1(G)$; the unimodular case

- Mathematics
- 2015

We consider the issue of describing all self-adjoint idempotents (projections) in $L^1(G)$ when $G$ is a unimodular locally compact group. The approach is to take advantage of known facts concerning… Expand

Fractional differential equations: alpha-entire solutions, regular and irregular singularities

- Mathematics, Physics
- 2008

We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional… Expand

Harmonic analysis and applications

- Mathematics, Computer Science
- Kybernetes
- 2012

This paper surveys briefly how harmonic analyis started and developed throughout the centuries to reach its modern status and its surprisingly wide range of applications. Expand

Fourier multipliers for certain spaces of functions with compact supports

- Mathematics
- 1977

This is perhaps the final word on how large overall the Fourier coefficients of continuous periodic functions can be. (See the remarks in Paley [,11] on this point.) Helgason [--53, Theorem 2,… Expand

Positive operator measures, generalised imprimitivity theorem, and their applications

- Mathematics, Physics
- 2005

Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and… Expand

Harmonic operators: the dual perspective

- Mathematics
- 2005

The study of harmonic functions on a locally compact group G has recently been transferred to a “non-commutative” setting in two different directions: Chu and Lau replaced the algebra L∞(G) by the… Expand