论文信息 - On the Fourier Spectra of Distributions in Clifford Analysis

On the Fourier Spectra of Distributions in Clifford Analysis

In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis, eventually leading to the introduction of four broad classes of new distributions in Euclidean space. In the current paper we continue the in-depth study of these distributions, more specifically the study of their behaviour in frequency space, thus extending classical results of harmonic analysis.

[1] F. Brackx,et al. HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS , 2005 .

[2] Tao Qian. Advances in analysis and geometry - new developments using Clifford algebras , 2004 .

[3] Fred Brackx,et al. Spherical Means and Distributions in Clifford Analysis , 2004 .

[4] Hennie De Schepper,et al. On the Fourier transform of distributions and differential operators in Clifford analysis , 2004 .

[5] Convolution kernels in Clifford analysis: old and new , 2005 .

[6] E. Stein,et al. Introduction to Fourier analysis on Euclidean spaces (PMS-32) , 1972 .

[7] Klaus Gürlebeck,et al. Quaternionic and Clifford Calculus for Physicists and Engineers , 1998 .

[8] J. Horváth. Singular integral operators and spherical harmonics , 1956 .

[9] F. Sommen,et al. Generalizations of Fueter’s theorem , 2002 .

[10] Richard Delanghe,et al. Some Remarks on the Principal Value Kernel in R m , 2002 .

[11] Fred Brackx,et al. SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS , 2003 .

[12] Spingroups and Spherical Means , 1986 .

[13] E. Stein,et al. Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[14] Tao Qian,et al. Advances in Analysis and Geometry , 2004 .

[15] John Ryan,et al. Dirac Operators in Analysis , 1999 .

[16] L. Schwartz. Théorie des distributions , 1966 .

[17] F. Sommen,et al. Clifford Algebra and Spinor-Valued Functions , 1992 .