{
  "id": "2104.10912",
  "version": "v1",
  "published": "2021-04-22T07:41:48.000Z",
  "updated": "2021-04-22T07:41:48.000Z",
  "title": "New parameters and Lebesgue-type estimates in greedy approximation",
  "authors": [
    "Fernando Albiac",
    "Jose L. Ansorena",
    "Pablo M. Berna"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to quantify the size of the Lebesgue constants $(L_m)_{m=1}^{\\infty}$ associated with the thresholding greedy algorithm in terms of a new generation of parameters that modulate accurately some features of a general basis. This fine-tuning of constants allows us to provide an answer to the question raised by Temlyakov in 2011 to find a natural sequence of greedy-type parameters for arbitrary bases in Banach (or quasi-Banach) spaces which combined linearly with the sequence of unconditionality parameters $(k_m)_{m=1}^{\\infty}$ determines the growth of $(L_m)_{m=1}^{\\infty}$. Multiple theoretical applications and computational examples complement our study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-22T07:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A65",
      "41A25",
      "41A46",
      "41A17",
      "46B15"
    ],
    "keywords": [
      "greedy approximation",
      "lebesgue-type estimates",
      "computational examples complement",
      "thresholding greedy algorithm",
      "general basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}