Abstract Harmonic Analysis

  title={Abstract Harmonic Analysis},
  author={Edwin Shields Hewitt and Kenneth A. Ross},
The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. E. Hewitt, K.A. Ross Abstract Harmonic Analysis 
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 formulaExpand
Classical Themes of Fourier Analysis
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 certainExpand
Operator theory in harmonic analysis
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 forExpand
Harmonic Analysis and Functional Equations
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 ofExpand
Projections in $L^1(G)$; the unimodular case
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 concerningExpand
Fractional differential equations: alpha-entire solutions, regular and irregular singularities
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 fractionalExpand
Harmonic analysis and applications
  • M. Filali
  • 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
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
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 $X$ andExpand
Harmonic operators: the dual perspective
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 theExpand