English

Minimal Operator Norms via Minimal Theta Functions

Functional Analysis 2018-06-12 v2 Classical Analysis and ODEs

Abstract

We investigate sharp frame bounds of Gabor frames with chirped Gaussians and rectangular lattices or, equivalently, the case of the standard Gaussian and general lattices. We prove that for even redundancy and standard Gaussian window the hexagonal lattice minimizes the upper frame bound using a result by Montgomery on minimal theta functions.

Cite

@article{arxiv.1608.01168,
  title  = {Minimal Operator Norms via Minimal Theta Functions},
  author = {Markus Faulhuber},
  journal= {arXiv preprint arXiv:1608.01168},
  year   = {2018}
}

Comments

14 pages

R2 v1 2026-06-22T15:11:04.276Z