The kernel of the generalized Clifford-Fourier transform and its generating function

被引：2

作者：

Lian, Pan ^{[1
,2
]}

Bao, Gejun ^{[1
]}

De Bie, Hendrik ^{[2
]}

Constales, Denis ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin, Peoples R China

[2] Univ Ghent, Dept Math Anal, Fac Engn & Architecture, Ghent, Belgium

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2017年 / 62卷 / 02期

关键词：

Clifford-Fourier transform; Laplace transform; Bessel function; generalized Fourier transform;

D O I：

10.1080/17476933.2016.1218851

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the generalized Clifford-Fourier transform using the Laplace transform technique. We give explicit expressions in the even dimensional case, we obtain polynomial bounds for the kernel functions and establish a generating function.

引用

页码：214 / 229

页数：16

共 16 条

[1]

[Anonymous], 1954, TABLES INTEGRAL TRAN

[2] Laguerre semigroup and Dunkl operators [J].

Ben Said, Salem ;

Kobayashi, Toshiyuki ;

Orsted, Bent .

COMPOSITIO MATHEMATICA, 2012, 148 (04) :1265-1336

[3] The mehler formula for the generalized Clifford-Hermite polynomials [J].

Brackx, F. ;

De Schepper, N. ;

Kou, K. I. ;

Sommen, F. .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2007, 23 (04) :697-704

[4] The Clifford-Fourier transform [J].

Brackx, F ;

De Schepper, N ;

Sommen, F .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2005, 11 (06) :669-681

[5] The two-dimensional Clifford-Fourier transform [J].

Brackx, Fred ;

De Schepper, Nele ;

Sommen, Frank .

JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2006, 26 (1-2) :5-18

[6]

Brackx F, 2013, TRENDS MATH, pXI

[7] A new construction of the Clifford-Fourier kernel [J].

Constales, Denis ;

De Bie, Hendrik ;

Lian, Pan .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2017, 23 (02) :462-483

[8] The Fractional Clifford-Fourier Kernel [J].

Craddock, M. J. ;

Hogan, J. A. .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2013, 19 (04) :683-711

[9] Generalized Fourier Transforms Arising from the Enveloping Algebras of sl(2) and osp(1|2) [J].

De Bie, Hendrik ;

Oste, Roy ;

van der Jeugt, Joris .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (15) :4649-4705

[10] On the Clifford-Fourier Transform [J].

De Bie, Hendrik ;

Xu, Yuan .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (22) :5123-5163

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