Elements of harmonic analysis, 5

Some topics in complex and harmonic analysis, 4

These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.

Some topics in complex and harmonic analysis, 3

These notes briefly consider some aspects of the Schwartz class of rapidly decreasing smooth functions, tempered distributions, and harmonic functions of polynomial growth.

M-正向量空间上的调和分析

Harmonic Analysis on the Space of M-positive Vectors

本文在由伸缩矩阵M定义的M-正向量空间上建立调和分析框架，引入Walsh函数类似物和Fourier变换，证明Poisson求和公式、Plancherel定理等，并刻画了函数及其Fourier变换均具紧支撑的Schwartz类类似物。

An elementary purely algebraic approach to generalized functions and operational calculus

The space of Schwartz distributions of finite order is represented as a factor space of the space of, what we call, Mikusinski functions. The point of Mikusinski functions is that they admit a multiplication by convergent Laurent series. It is shown that this multiplication provides a natural simple basis for Heaviside's operational calculus.

Invertibility In the Sense of Ehrenpreis

We consider zero sets of entire functions belonging to the Schwartz algebra. This algebra is defined as the Fourier-Laplace transform image of the space of all distributions compactly supported on the real line. We study the conditions under which given complex sequence forms zero set of some invertible in the sense of Ehrenpreis element of the Schwartz algebra (slowly decreasing function).

(k, a)-广义傅里叶变换的Schwartz空间及共形群的最简表示

The Schwartz space for the $ (k, a) $-generalized Fourier transform and the minimal representation of the conformal group

本文研究了(k,a)-变形调和分析框架下的Schwartz空间类，定义了(k,a)-广义Schwartz空间，并确定了其在共形群最简表示中的平滑向量空间。