On generalized Hilbert transforms and their interaction with the Radon transform in Clifford analysis

2007 ◽  
Vol 30 (9) ◽  
pp. 1071-1092 ◽  
Author(s):  
Fred Brackx ◽  
Bram De Knock ◽  
Hennie De Schepper
Keyword(s):  
Radon Transform ◽  
Clifford Analysis ◽  
Hilbert Transforms

scholarly journals Generalized multidimensional Hilbert transforms in Clifford analysis

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Fred Brackx ◽  
Bram De Knock ◽  
Hennie De Schepper
Keyword(s):  
Sobolev Spaces ◽  
Hilbert Transform ◽  
Clifford Analysis ◽  
Hilbert Transforms ◽  
Singular Operators ◽  
The Hilbert Transform

Two specific generalizations of the multidimensional Hilbert transform in Clifford analysis are constructed. It is shown that though in each of these generalizations some traditional properties of the Hilbert transform are inevitably lost, new bounded singular operators emerge on Hilbert or Sobolev spaces ofL2-functions.

scholarly journals Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis

2013 ◽  
Vol 58 (8) ◽  
pp. 1057-1069 ◽  
Author(s):  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes ◽  
Fred Brackx ◽  
Hennie De Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Hilbert Transforms ◽  
Quaternionic Clifford Analysis

scholarly journals Hilbert Transforms in Clifford Analysis

2010 ◽  
pp. 163-187 ◽  
Author(s):  
Fred Brackx ◽  
Bram De Knock ◽  
Hennie De Schepper
Keyword(s):  
Clifford Analysis ◽  
Hilbert Transforms
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