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arXiv · 2004.02152

Orbits of bounded bijective operators and Gabor frames

Rosario Corso
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Abstract

This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete Gabor frames, with some ordering over $\mathbb{Z}$, which are orbits of bounded operators on $L^2(\mathbb{R})$. Two classes of overcomplete Gabor frames which cannot be ordered over $\mathbb{Z}$ and represented by orbits of operators in $GL(L^2(\mathbb{R}))$ are given. Some results about operator representation are stated in a general context for arbitrary frames, covering also certain wavelet frames.

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Rosario Corso. 2020-04-05. Orbits of bounded bijective operators and Gabor frames. https://doi.org/10.1007/s10231-020-00988-1

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