Gabor frame operator for the Cauchy kernel

Yurii Belov; Aleksei Kulikov; Yurii Lyubarskii

Gabor frame operator for the Cauchy kernel

Complex Variables 2022-12-20 v1

Authors: Yurii Belov , Aleksei Kulikov , Yurii Lyubarskii

Abstract

We obtain frame bounds estimates and the Gabor frame operator $S=S^{\alpha,\beta}$ for Gabor frames generated by the Cauchy kernel. In addition we find the explicit expression for the canonical dual window for all values of the lattice parameters $\alpha,\beta$ , $\alpha\beta\leq 1$ .

Keywords

frame theory

Cite

@article{arxiv.2212.08915,
  title  = {Gabor frame operator for the Cauchy kernel},
  author = {Yurii Belov and Aleksei Kulikov and Yurii Lyubarskii},
  journal= {arXiv preprint arXiv:2212.08915},
  year   = {2022}
}

Comments

Submitted August 15, 2022 to Ufa Mathematical Journal

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