A new construction of the Clifford-Fourier kernel

被引：19
作者：
Constales, Denis [1 ]
De Bie, Hendrik [1 ]
Lian, Pan [1 ,2 ]
机构：
[1] Univ Ghent, Fac Engn & Architecture, Dept Math Anal, Galglaan 2, B-9000 Ghent, Belgium
[2] Harbin Inst Technol, Dept Math, West Da Zhi St 92, Harbin 150001, Peoples R China
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2017年 / 23卷 / 02期
关键词：
Clifford-Fourier transform; Laplace transform; Bessel function; Plane wave decomposition;
D O I：
10.1007/s00041-016-9476-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse Laplace transform may be computed and we obtain the explicit expression for the kernel as a finite sum of Bessel functions. We equally obtain the plane wave decomposition and find new integral representations for the kernel in all dimensions. Finally we define and compute the formal generating function for the even dimensional kernels.
引用
收藏
页码：462 / 483
页数：22
相关论文
共 16 条
[1]  
[Anonymous], 1954, TABLES INTEGRAL TRAN
[2]   The Clifford-Fourier transform [J].
Brackx, F ;
De Schepper, N ;
Sommen, F .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2005, 11 (06) :669-681
[3]  
Brackx F., 1982, RES NOTES MATH
[4]   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
[5]   The Clifford-Fourier integral kernel in even dimensional Euclidean space [J].
Brackx, Fred ;
De Schepper, Nele ;
Sommen, Frank .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 365 (02) :718-728
[6]   The Fractional Clifford-Fourier Kernel [J].
Craddock, M. J. ;
Hogan, J. A. .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2013, 19 (04) :683-711
[7]   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
[8]   The Fractional Clifford-Fourier Transform [J].
De Bie, Hendrik ;
De Schepper, Nele .
COMPLEX ANALYSIS AND OPERATOR THEORY, 2012, 6 (05) :1047-1067
[9]   The Class of Clifford-Fourier Transforms [J].
De Bie, Hendrik ;
De Schepper, Nele ;
Sommen, Frank .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2011, 17 (06) :1198-1231
[10]   On the Clifford-Fourier Transform [J].
De Bie, Hendrik ;
Xu, Yuan .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (22) :5123-5163
12