Coorbit space theory for quasi-Banach spaces

• Autorzy: Holger Rauhut
• Języki publikacji: EN

Abstrakty

EN

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig 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 ≤ ∞.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 42C15: General harmonic expansions, frames
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 180
• Numer: 3
• Strony: 237-253

Daty

wydano

2007

Twórcy

autor

Holger Rauhut

• NuHAG, Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria

Identyfikatory

DOI

10.4064/sm180-3-4