Related papers: Some topics in complex and harmonic analysis, 2
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
These informal notes deal with a number of questions related to sums and integrals in analysis.
Fourier Series is the second 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 as partial…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
In these notes we briefly consider various situations related to infinite commutative semigroups, connected to convolutions and Fourier transforms.
These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.
These notes deal with a few properties of convolutions in the role of approximations to the identity.
Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
These informal notes are concerned with sums and averages in various situations in analysis.
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
We extend the Reed Dawson identity for Knuth's old sum with a complex parameter, and we offer two separate hypergeometric series-based proofs of this generalization, and we apply this generalization to introduce binomial-harmonic sum…
The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis of several variables and Riemann-Stieltjes integration are also included.
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to…
In this article, we continue our recent investigations on bilinear sums and additive energies with modular square roots. Here we improve our recent results for the case when the ranges of variables are large. We use these results to make…