Spherical means, distributions and convolution operators in Clifford analysis

被引：15

作者：

Brackx, F ^{[1
]}

Delanghe, R ^{[1
]}

Sommen, F ^{[1
]}

机构：

[1] State Univ Ghent, Dept Math Anal, B-9000 Ghent, Belgium

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2003年 / 24卷 / 02期

关键词：

spherical means; distributions; convolution operators; Clifford analysis;

D O I：

10.1142/S0252959903000141

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New higher dimensional distributions are introduced in the framework of Clifford analysis. They complete the picture already established in previous work, offering unity and structural clarity. Amongst them are the building blocks of the principal value distribution, involving spherical harmonics, considered by Horvath and Stein.

引用

页码：133 / 146

页数：14

共 50 条

[11] Hankel convolution operators on entire functions and distributions
Belhadj, M
Betancor, JJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 276 (01) : 40 - 63
[12] Hypoelliptic Jacobi Convolution Operators on Schwartz Distributions
J. J. Betancor
J. D. Betancor
J. M. R. Méndez
[J]. Positivity, 2004, 8 : 407 - 422
[13] FAST APPROXIMATION BY MEANS OF CONVOLUTION-OPERATORS
SIKKEMA, PC
[J]. PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1981, 84 (04): : 431 - 444
[14] The cone-beam transform and spherical convolution operators
Quellmalz, Michael
Hielscher, Ralf
Louis, Alfred K.
[J]. INVERSE PROBLEMS, 2018, 34 (10)
[15] Spherical convolution operators in spaces of variable Holder order
Vakulov, B. G.
[J]. MATHEMATICAL NOTES, 2006, 80 (5-6) : 645 - 657
[16] Convolution kernels in Clifford analysis: Old and new
Brackx, F
De Schepper, H
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2005, 28 (18) : 2173 - 2182
[17] Clifford analysis techniques for spherical PDE
Liu, H
Ryan, J
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2002, 8 (06) : 535 - 563
[18] Clifford Analysis Techniques for Spherical PDE
Hong Liu
John Ryan
[J]. Journal of Fourier Analysis and Applications, 2002, 8 : 535 - 564
[19] On Operators and Elementary Functions in Clifford Analysis
Sproessig, W.
[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 1999, 18 (02): : 349 - 360
[20] Discrete Dirac Operators in Clifford Analysis
Nelson Faustino
Uwe Kähler
Frank Sommen
[J]. Advances in Applied Clifford Algebras, 2007, 17 : 451 - 467

← 1 2 3 4 5 →