{
  "id": "1804.10984",
  "version": "v1",
  "published": "2018-04-29T19:57:40.000Z",
  "updated": "2018-04-29T19:57:40.000Z",
  "title": "Riesz bases from orthonormal bases by replacement",
  "authors": [
    "Laura De Carli",
    "Julian Edward"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given an orthonormal basis $ {\\mathcal V}= \\{v_j\\} _{j\\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\\mathcal B}=\\{w_j\\}_{j\\in N}$, we consider the sets $ {\\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\\, v_N$ with vectors $w_1,\\, ...,\\, w_N$. We show necessary and sufficient conditions that ensure that the sets $ {\\mathcal B}_N$ are Riesz bases of $H$ and we estimate the frame constants of the $ {\\mathcal B}_N$. Then, we prove conditions that ensure that $ {\\mathcal B}$ is a Riesz basis. Applications to the construction of exponential bases on domains of $ R^d$ are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-29T19:57:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz basis",
      "orthonormal basis",
      "replacement",
      "unit vectors",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}