{
  "id": "2002.11512",
  "version": "v1",
  "published": "2020-02-21T16:53:22.000Z",
  "updated": "2020-02-21T16:53:22.000Z",
  "title": "Construction of the $ K{S^p}$ spaces on $\\mathbb{R}^\\infty$ and Separable Banach Spaces",
  "authors": [
    "Hemanta Kalita",
    "Tepper L. Gill",
    "Bipan Hazarika",
    "Timothy Myers"
  ],
  "comment": "pages 33",
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to construct a new class of separable Banach spaces $KS^p[\\mathbb{R}^{\\infty}], \\; 1\\leq p \\leq \\infty$. Each of these spaces contain the $ L^p[\\mathbb{R}^\\infty] $ spaces, as well as the space $\\mfM[\\mathbb{R}^\\iy]$, of finitely additive measures as dense continuous compact embeddings. These spaces are of interest because they also contain the Henstock-Kurzweil integrable functions on $\\mathbb{R}^\\iy$. We will construct a canonical class of Kuelb-Steadman spaces $KS^p[\\mathcal{B}], \\; 1\\leq p \\leq \\infty$, where $\\mathcal{B}$ is separable Banach space. %and come again to $K{S^p}[\\mathbb{R}^\\infty].$ Finally, we offer a interesting approach to the Fourier transform on $K{S^p}[\\mathbb{R}^{\\infty}]$ and $KS^p[\\mathcal{B}]$. % an application of $K{S^p}[\\mathbb{R}^{\\infty}].$ %Further we find $K{S^2}[\\mathbb{R}^{\\infty}] $ satisfies the requirement for Heisenberg and Schr\\\"{o}dinger representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-21T16:53:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A39",
      "46B03",
      "46B20",
      "46B25"
    ],
    "keywords": [
      "separable banach space",
      "construction",
      "dense continuous compact embeddings",
      "spaces contain",
      "fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}