{
  "annotation_id": "340c0a76-f48e-478f-b628-987d99056b5f",
  "date_created": "2026-03-02T18:01:21.736000Z",
  "date_modified": "2026-03-02T18:01:21.736000Z",
  "file_hash": "623121bfc21b906c473a4ecbb48fed942ece3600945ccbf9a6bb2586ff01917e",
  "private": false,
  "record": {
    "abstract": "The study concerns a special symbolic calculus of interest for signal\nanalysis. This calculus associates functions on the time-frequency half-plane\nf\u003e0 with linear operators defined on the positive-frequency signals. Full\nattention is given to its construction which is entirely based on the study of\nthe affine group in a simple and direct way. The correspondence rule is\ndetailed and the associated Wigner function is given. Formulas expressing the\nbasic operation (star-bracket) of the Lie algebra of symbols, which is\nisomorphic to that of the operators, are obtained. In addition, it is shown\nthat the resulting calculus is covariant under a three-parameter group which\ncontains the affine group as subgroup. This observation is the starting point\nof an investigation leading to a whole class of symbolic calculi which can be\nconsidered as modifications of the original one.",
    "arxiv_id": "physics/9708027",
    "authors": [
      "J. Bertrand",
      "P. Bertrand"
    ],
    "categories": [
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.532484",
    "journal_ref": "J.Math.Phys. 39 (1998) 4071-4090",
    "title": "Symbolic calculus on the time-frequency half-plane",
    "url": "https://arxiv.org/abs/physics/9708027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "33493b8d-89eb-4136-895a-e65aecf0f3fd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}