Generalized multidimensional Hilbert transforms in Clifford analysis

DOI10.1155/IJMMS/2006/98145zbMath1114.30050OpenAlexW2103058599MaRDI QIDQ884187

Hennie De Schepper, Bram De Knock, Fred Brackx

Publication date: 13 June 2007

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/53146

zbMATH Keywords

Fourier transformHilbert transformClifford analysishomogeneous polynomialsthe convolution kernelthe distributionsthe Hardy space

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

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Cites Work

• An introduction to Dirac operators on manifolds
• On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis
• Clifford wavelets, singular integrals, and Hardy spaces
• Spherical means, distributions and convolution operators in Clifford analysis
• Szegő projections for Hardy spaces of monogenic functions and applications
• On some properties of the Hilbert transform in Euclidean space
• Hilbert-Dirac operators in Clifford analysis
• Advances in analysis and geometry. New developments using Clifford algebras. Based on the satellite conference to the ICM 2002 in Beijing, Macau, China, August 15--18, 2002
• A calculus scheme for Clifford distributions
• Multi-vector spherical monogenics, spherical means and distributions in Clifford analysis
• Some Remarks on the Principal Value Kernel in R m
• Singular Integral Operators and Spherical Harmonics
• Hypercomplex fourier and laplace transforms II
• On the Fourier transform of distributions and differential operators in Clifford analysis
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