Coorbit space theory for quasi-Banach spaces

By Holger Rauhut. 2005

62 citations recorded by the source corpus.

We generalize the classical coorbit space theory developed by Feichtinger and Grochenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces M p,q m , 0 < p,q 1 .

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e1e68945d13328fa15c74170d393803231605596

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type (2010, background): “An extension to quasi-Banach spaces, similar to the classical case in [42], is presently under investigation.”
New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets (2011, methodology): “Here, the main difficulty lies in the fact that, in the (quasi-)Banach situation, a coorbit space is defined as a certain retract of a Wiener-Amalgam space; see [34].”
Generalized coorbit theory, Banach frames, and the relation to α‐modulation spaces (2008, background): “In [35] the classical coorbit theory was generalized with the aim of to also treating quasi-Banach spaces.”
Remarks on Fourier multipliers and applications to the Wave equation (2008, background): “The definition above is extended to the cases 0 < p, q < 1 in [3]; here the window function g ∈ S satisfies supp ĝ ⊂ {|ξ| ≤ 1}, see also [11] for the quasi-Banach case in the global component L.”
Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits (2010, methodology): “Acknowledgement: The author would like to thank Holger Rauhut, Martin Schäfer, Benjamin Scharf, and Hans Triebel for valuable discussions, a critical reading of preliminary versions of this manuscript and for several hints how to improve it.”