Related papers: Elements of harmonic analysis
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
This is a continuation of our previous work in bi-free harmonic analysis for commuting left and right variables. Here we analyze the bi-free partial S-transform and use the results to study limit theorems and infinite divisibility relative…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so…
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
Topics in the description of the properties of charmonium states are reviewed with an emphasis on specific theoretical ideas and methods of relating those properties to the underlying theory of Quantum Chromodynamics.
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
This note reviews complex and real techniques in harmonic analysis. We describe a common source of both approaches rooted in the covariant transform generated by the affine group. Keywords: wavelet, coherent state, covariant transform,…
In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic analysis in the last 90 years, reviewing, on the one hand, the…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
The area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives,…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
These informal notes briefly discuss various aspects of Cantor sets.
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
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…