Related papers: A theorem concerning Fourier transforms: A survey
In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R^+, which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This…
The main purpose of this article is to survey on some key elements of a recent $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$, which was mainly inspired by the work of Bayart and Helson on ordinary Dirichlet…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
This article, which grew out of my lecture at the conference "Analysis and Applications: A Conference in Honor of Elias M. Stein" in May 2011, is intended to give an overview on a collection of results which have been obtained jointly with…
This brief note aims at condensing some results on the 32-point approximate DFT and discussing its arithmetic complexity.
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then the harmonic…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over…
Let G/H be a reductive symmetric space and K a maximal compact subgroup of G. We study Fourier transforms of compactly supported K-finite distributions on G/H and characterize the image of the space of such distributions.
We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.
In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
Edwards transformations relating inertial frames with arbitrary clock synchronization are reminded and put in more general setting. Their group theoretical context is described.
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the action of GL(2,Z) on the Macdonald polynomials at…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…