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arXiv · 1705.04028

Wave packet frames generated by hyponormal operators on $L^2(\mathbb{R})$

Lalit K. Vashisht
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Abstract

In this paper we study frame-like properties of a wave packet system by using hyponormal operators on $L^2(\mathbb{R})$. We present necessary and sufficient conditions in terms of relative hyponormality of operators for a system to be a wave packet frame in $L^2(\mathbb{R})$. A characterization of hyponormal operators by using tight wave packet frames is proved. This is different from a method proved by Djordjevi$\acute{c}$ by using the Moore-Penrose inverse of a bounded linear operator with a closed range. The linear combinations of wave packet frames generated by hyponormal operators are discussed.

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Lalit K. Vashisht. 2017-05-11. Wave packet frames generated by hyponormal operators on $L^2(\mathbb{R})$. https://arxiv.org/abs/1705.04028

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