scholarly journals On a Regularization Scheme for Linear Operators in Distribution Spaces with an Application to the Spherical Radon Transform

2005 ◽  
Vol 65 (4) ◽  
pp. 1369-1387 ◽  
Author(s):  
Thomas Schuster ◽  
Eric Todd Quinto
Keyword(s):  
Radon Transform ◽  
Linear Operators ◽  
Regularization Scheme ◽  
Distribution Spaces ◽  
Spherical Radon Transform

scholarly journals The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Joachim Toft
Keyword(s):  
Operator Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Modulation Spaces ◽  
Zak Transform ◽  
Periodic Functions ◽  
Distribution Spaces ◽  
Necessary And Sufficient

AbstractWe characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjugations by Zak transforms.

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