Related papers: Some topics in complex and harmonic analysis
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral graph theory. In addition, several generalizations of these…
We derive some identities and relations and extremal problems and minimization and Fourier development involving of integral Legendre polynomials.
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
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…
This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting behaviour of these sets as those with in case of a…
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…
The Funk, cosine, and sine transforms on the unit sphere are indispensable tools in integral geometry. They are also known to be interesting objects in harmonic analysis. The aim of the paper is to extend basic facts about these transforms…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…
In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…