# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "The homogeneous approximation property and localized Gabor frames"

#### Neuhauser, Markus

The homogeneous approximation property (HAP) has been introduced in order to describe the locality of Gabor expansions in the Hilbert space $L^{2}({\mathbb{R}}^{d})$. The HAP property is established for families of modulation spaces. Instead of the more recent theory of localized frames (Groechenig in J Fourier Anal Appl 10(2):105-132) which relies on Wiener pairs of Banach algebras of matrices, our approach is based on the constructive principles established in Feichtinger (J Funct Anal 86:307-340, Monatsh Math 108:129-148, Groechenig (Monatsh Math 112:1-41, using the fact that generalized modulation spaces are coorbit spaces with respect to the Schroedinger representation of the Heisenberg group (cf. Feichtinger in Wavelets-a tutorial in theory and applications, Academic Press, Boston, pp 359-397). For the (non-canonical) dual frames obtained constructively in this way the HAP property is verified.

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