Some topics concerning harmonic analysis on metric spaces

Some topics in complex and harmonic analysis

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

Hankel determinants of harmonic numbers and related topics

We give an overview of known results about Hilbert matrices from the point of view of orthogonal polynomials and compute Hankel determinants of harmonic numbers and related topics.

Elements of harmonic analysis, 3

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

Elements of harmonic analysis

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

Some Bernstein functions and integral representations concerning harmonic and geometric means

It is general knowledge that the harmonic mean $H(x,y)=\frac2{\frac1x+\frac1y}$ and that the geometric mean $G(x,y)=\sqrt{xy}\,$, where $x$ and $y$ are two positive numbers. In the paper, the authors show by several approaches that the harmonic mean $H_{x,y}(t)=H(x+t,y+t)$ and the geometric mean $G_{x,y}(t)=G(x+t,y+t)$ are all Bernstein functions of $t\in(-\min\{x,y\},\infty)$ and establish integral representations of the means $H_{x,y}(t)$ and $G_{x,y}(t)$.

Hyponormal Toeplitz Operators with Non-Harmonic Algebraic Symbol

We generalize recent results of Fleeman and Liaw on the topic of hyponormal Toeplitz operators acting on the Bergman space of the unit disk.

关于傅里叶变换的一个定理：综述

A theorem concerning Fourier transforms: A survey

本文综述了Hardy关于傅里叶变换定理对调和分析领域的影响，包括其推广和相关领域的联系。

调和分析中的不确定性原理——精选主题讲义

The Uncertainty Principle in Harmonic Analysis -- Lecture Notes on Selected Topics

本文通过 Fourier 级数与变换的唯一性和重建问题、频谱间隙影响及对数可积性在逼近与拟解析性中的作用，探讨了不确定性原理的多个经典表现，涵盖 Paley-Wiener 定理等核心结果。

关于涉及调和数与斜调和数的若干级数

On Some Series Involving Harmonic and Skew-Harmonic Numbers

本文以闭式形式评估了涉及调和数与斜调和数的两类级数，解决了两个开放问题，并研究了Hardy级数。

Some questions related to fractals

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

Some remarks concerning integrals of curvature on curves and surfaces

In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using quarternions or Clifford algebras. These topics came up in "Analysis of and on Uniformly Rectifiable Sets" (with Guy David, American Mathematical Society, 1993), and here we describe some of the basic points involved. A presentation based on this paper was made at the AMS Special Session "Surface Geometry and Shape Perception" (Hoboken, 2001).

On a Steklov spectrum in Electromagnetics

After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning natural Steklov boundary value problems for the curlcurl operator. Moreover, we explicitly compute eigenvalues and eigenfunctions in the unit ball of the three-dimensional Euclidean space by using classical vector spherical harmonics.

Discrete harmonic analysis associated with Jacobi expansions I: the heat semigroup

In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(α,β)$. Particularly, we give the solution $W^{(α,β)}_t$, $t\ge 0$, and some properties of the heat equation related to the operator $J^{(α,β)}-I$, where $J^{(α,β)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator. These results will be a consequence of a much more general theorem concerning the solution of the heat equation for Jacobi matrices. In addition, we also prove the positivity of the operator $W^{(α,β)}_…

An elementary proof of the meromorphy of the integral of f^z for real-analytic f

A proof of a result of Atiyah and Bernstein/Gelfand concerning the title's topic is given that relies solely on the recent elementary resolution of singularities algorithm of the author.