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Orbits of bounded bijective operators and Gabor frames
Annali di Matematica Pura ed Applicata ( IF 0.959 ) Pub Date : 2020-05-20 , DOI: 10.1007/s10231-020-00988-1
Rosario Corso

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.
更新日期:2020-05-20

 

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