{
  "id": "1907.00466",
  "version": "v1",
  "published": "2019-06-30T21:24:05.000Z",
  "updated": "2019-06-30T21:24:05.000Z",
  "title": "Quantum harmonic analysis on lattices and Gabor multipliers",
  "authors": [
    "Eirik Skrettingland"
  ],
  "comment": "35 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We develop a theory of quantum harmonic analysis on lattices in $\\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and operators we develop a version of harmonic analysis for these objects. We prove analogues of results from classical harmonic analysis and the quantum harmonic analysis of Werner, including Tauberian theorems and a Wiener division lemma. Gabor multipliers from time-frequency analysis are described as convolutions in this setting. The quantum harmonic analysis is thus a conceptual framework for the study of Gabor multipliers, and several of the results include results on Gabor multipliers as special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-30T21:24:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "47B10",
      "35S05",
      "42B05",
      "43A32"
    ],
    "keywords": [
      "quantum harmonic analysis",
      "gabor multipliers",
      "wiener division lemma",
      "tauberian theorems",
      "convolutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}