On an Inversion Formula for the Fourier Transform on Distributions by Means of Gaussian Functions

被引：2

作者：

Gonzalez, B. J. ^{[1
]}

Negrin, E. R. ^{[1
]}

机构：

[1] ULL, Fac Ciencias, Dept Anal Matemat, Campus Anchieta, ES-38271 San Cristobal la Laguna, Tenerife, Spain

来源：

FILOMAT | 2018年 / 32卷 / 06期

关键词：

Fourier transform; Distributions; Inversion formula; Gaussian functions; Convolution equations; Differential equations; REPRESENTATION; CONVOLUTION;

D O I：

10.2298/FIL1806327G

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Gaussian functions are useful in order to establish inversion formulae for the classical Fourier transform. In this paper we show that they also are helpful in order to obtain a Fourier inversion formula for the distributional case.

引用

页码：2327 / 2334

页数：8

共 16 条

[1] Representation of the Fourier Transform of Distributions in K′p,k′ k < 0. [J].

Abdullah, Saleh .

FILOMAT, 2016, 30 (06) :1519-1524

[2]

[Anonymous], 1977, Undergraduate Texts in Mathematics

[3]

[Anonymous], 1966, ADDISON WESLEY SERIE

[4] CONVOLUTION OVER THE SPACES-G'(K) [J].

GONZALEZ, BJ ;

NEGRIN, ER .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 190 (03) :829-843

[5] FOURIER-TRANSFORM OVER THE SPACES G(K)' [J].

GONZALEZ, BJ ;

NEGRIN, ER .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 194 (03) :780-798

[6] ON THE STRUCTURE OF INVERTIBLE ELEMENTS OF THE CONVOLUTION ALGEBRA G'(K) [J].

GONZALEZ, BJ ;

NEGRIN, ER .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 195 (02) :506-516

[7] Distributional representation of a Fourier inversion formula [J].

Hayek, N ;

Gonzalez, BJ ;

Negrin, ER .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2005, 16 (01) :21-28

[8] A family of Wiener transforms associated with a pair of operators on Hilbert space [J].

Hayek, N. ;

Srivastava, H. M. ;

Gonzalez, B. J. ;

Negrin, E. R. .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (01) :1-8

[9]

Hormander L, 1990, DISTRIBUTION THEORY, VSecond

[10]

Lang S., 1974, ANALYSIS 1

← 1 2 →