{
  "annotation_id": "30789325-7539-4029-bc66-26d0ba292632",
  "date_created": "2026-03-02T18:02:34.732000Z",
  "date_modified": "2026-03-02T18:02:34.732000Z",
  "file_hash": "0eeeacf674764a91db9470144689644184435152ad5e63f05bb83613e51fb9f1",
  "private": false,
  "record": {
    "abstract": "We characterize the elements of generalized Gelfand Shilov spaces in terms of\nthe coefficients of their Fourier-Hermite expansion. The technique we use can\nbe applied both in quasianalytic and nonquasianalytic case. The\ncharacterizations imply the kernel theorems for the dual spaces. The cases when\nthe test space is quasianalytic are important in quantum field theory with a\nfundamental length, see for example papers of E.Bruning and S.Nagamachi,where\nit was conjectured that the properties of the space of Fourier hyper functions,\nwhich is isomorphic with S^1_1 are well adapted for the use in the theory.",
    "arxiv_id": "quant-ph/0701041",
    "authors": [
      "Z. Lozanov--Crvenkovic",
      "D. Perisic"
    ],
    "categories": [
      "quant-ph",
      "math.FA"
    ],
    "title": "Hermite Expansions of Elements of Generalized Gelfand-Shilov space",
    "url": "https://arxiv.org/abs/quant-ph/0701041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "370f3bb1-c510-4376-a9ab-b4c607db082f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}