Related papers: Elements of harmonic analysis, 3

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…

The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.

These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…

This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces…

By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson…

On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…

These notes briefly consider some aspects of the Schwartz class of rapidly decreasing smooth functions, tempered distributions, and harmonic functions of polynomial growth.

We discuss convergence in the Fourier algebra A(G) of a locally compact group G and provide a new characterisation of the local spectral sets of G.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

In this work we construct harmonic analysis on free Abelian groups of rank $2$, namely: we construct and investigate spaces of functions and distributions, Fourier transforms, actions of discrete and extended discrete Heisenberg groups. In…

We obtain a characterisation of the Fourier transform on the space of Schwartz-Bruhat functions on locally compact Abelian groups. The result states that any appropriately additive bijection of the Schwartz space onto itself, which…