相关论文: Elements of harmonic analysis
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…
Complex functions $\chi (m)$ where $m$ belongs to a Galois field $GF(p^ \ell)$, are considered. Fourier transforms, displacements in the $GF(p^ \ell) \times GF(p^ \ell)$ phase space and symplectic $Sp(2,GF(p^ \ell))$ transforms of these…
These notes are concerned with the Schwartz class of rapidly decreasing smooth functions on R^n, Fourier transforms, etc.
In this paper we review some connections between harmonic analysis and the modern theory of automorphic forms. We indicate in some examples how the study of problems of harmonic analysis brings us to the important objects of the theory of…
We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more important in high-energy astronomy. Many sophisticated tools are available for data…
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.
These informal notes deal with some topics related to analysis on metric spaces.
We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
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…
These notes briefly consider some aspects of the Schwartz class of rapidly decreasing smooth functions, tempered distributions, and harmonic functions of polynomial growth.
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
This short note contains elementary evaluations of some Euler sums.
We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.…
This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…