Related papers: Elements of harmonic analysis, 2
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
These notes are concerned with the Schwartz class of rapidly decreasing smooth functions on R^n, Fourier transforms, etc.
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.
These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
These notes briefly consider some aspects of the Schwartz class of rapidly decreasing smooth functions, tempered distributions, and harmonic functions of polynomial growth.
Complex functions $\chi (m)$ where $m$ belongs to a Galois field $GF(p^ \ell)$, are considered. Fourier transforms, displacements in the $GF(p^ \ell) \times GF(p^ \ell)$ phase space and symplectic $Sp(2,GF(p^ \ell))$ transforms of these…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
This paper is a companion paper to [G4], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [G4] are stated in a rather general…
A q-version of the Fourier transformation and some of its properties are discussed.
These notes deal with a few properties of convolutions in the role of approximations to the identity.
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
These informal notes deal with a number of questions related to sums and integrals in analysis.
This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform…