论文信息 - HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

Around the central theme of "square root" of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.

F. Brackx | H. De Schepper

[1] Richard Delanghe,et al. On some properties of the Hilbert transform in Euclidean space , 2004 .

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

[3] J. Horváth. On some composition formulas , 1959 .

[4] A. Zygmund,et al. Singular Integral Operators and Differential Equations , 1957 .

[5] J. Alvarez,et al. Optimal spaces for the S’-convolution with the Marcel Riesz kernels and the N-dimensional Hilbert kernel , 1999 .

[6] M. Riesz. L'intégrale de Riemann-Liouville et le problème de Cauchy , 1949 .

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

[8] J. Ryan. Clifford Algebras in Analysis and Related Topics , 1995 .

[9] F. Sommen. Some connections between clifford analysis and complex analysis , 1982 .

[10] F. Sommen. Clifford Analysis and Integral Geometry , 1992 .

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

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