scholarly journals Kernel theorems in coorbit theory

2019 ◽  
Vol 6 (11) ◽  
pp. 346-364
Author(s):  
Peter Balazs ◽  
Karlheinz Gröchenig ◽  
Michael Speckbacher
Keyword(s):  
Coorbit Theory

scholarly journals A Primer on Coorbit Theory

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Eirik Berge
Keyword(s):  
Locally Compact Group ◽  
Unitary Representations ◽  
Modulation Spaces ◽  
Compact Groups ◽  
Locally Compact ◽  
Coorbit Spaces ◽  
Core Feature ◽  
Coorbit Theory ◽  
Main Ideas ◽  
Conceptual Difficulties

AbstractCoorbit theory is a powerful machinery that constructs a family of Banach spaces, the so-called coorbit spaces, from well-behaved unitary representations of locally compact groups. A core feature of coorbit spaces is that they can be discretized in a way that reflects the geometry of the underlying locally compact group. Many established function spaces such as modulation spaces, Besov spaces, Sobolev–Shubin spaces, and shearlet spaces are examples of coorbit spaces. The goal of this survey is to give an overview of coorbit theory with the aim of presenting the main ideas in an accessible manner. Coorbit theory is generally seen as a complicated theory, filled with both technicalities and conceptual difficulties. Faced with this obstacle, we feel obliged to convince the reader of the theory’s elegance. As such, this survey is a showcase of coorbit theory and should be treated as a stepping stone to more complete sources.

scholarly journals Frames and Coorbit Theory on Homogeneous Spaces with a Special Guidance on the Sphere

2007 ◽  
Vol 13 (4) ◽  
pp. 387-403 ◽  
Author(s):  
Stephan Dahlke ◽  
Gabriele Steidl ◽  
Gerd Teschke
Keyword(s):  
Homogeneous Spaces ◽  
Coorbit Theory

Shearlet Coorbit Theory

2015 ◽  
pp. 83-147
Author(s):  
Stephan Dahlke ◽  
Sören Häuser ◽  
Gabriele Steidl ◽  
Gerd Teschke
Keyword(s):  
Coorbit Theory

Generalized coorbit theory, Banach frames, and the relation to α-modulation spaces

2007 ◽  
Vol 96 (2) ◽  
pp. 464-506 ◽  
Author(s):  
Stephan Dahlke ◽  
Massimo Fornasier ◽  
Holger Rauhut ◽  
Gabriele Steidl ◽  
Gerd Teschke
Keyword(s):  
Modulation Spaces ◽  
Banach Frames ◽  
Coorbit Theory
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