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On generalized Hilbert transforms and their interaction with the Radon transform in Clifford analysis
Author(s) -
Brackx Fred,
De Knock Bram,
De Schepper Hennie
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.826
Subject(s) - hilbert transform , mathematics , radon transform , context (archaeology) , clifford analysis , hilbert space , clifford algebra , algebra over a field , pure mathematics , mathematical analysis , statistics , spectral density , dirac operator , paleontology , biology
Abstract The present paper deals with the interaction between the multidimensional Hilbert transform and the Radon transform in Clifford analysis, both transforms being protagonists in multidimensional signal analysis theory. In an attempt to complete the picture, we consider in particular the action of the Radon transform on two types of generalized Hilbert operators, which have been constructed in the context of some well‐established families of Clifford distributions. Copyright © 2007 John Wiley & Sons, Ltd.