相关论文: Some topics in complex and harmonic analysis

This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.

We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories.…

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.

A discussion of methods of nonisotropic fine quantitative complex analysis on lineally convex domains of finite type is given. The needed support functions with best possible estimates are considered together with the estimation of their…

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.

The analysis of multi-dimensional graph signals on complex structured domains remains a fundamental challenge,

The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.

We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…

This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…

In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…

This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,…

This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…

In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.

These notes are concerned with the Schwartz class of rapidly decreasing smooth functions on R^n, Fourier transforms, etc.

We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.

We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…

These informal notes deal with a number of questions related to sums and integrals in analysis.

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.