{
  "id": "1703.04045",
  "version": "v1",
  "published": "2017-03-11T23:53:41.000Z",
  "updated": "2017-03-11T23:53:41.000Z",
  "title": "Stechkin's problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applications",
  "authors": [
    "Vladyslav Babenko",
    "Yuliya Babenko",
    "Nadiia Kriachko"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we solve the problem of approximating functionals $(\\varphi(A)x, f)$ (where $\\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $\\psi (A)$ of the operator $A$. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate $|(\\varphi(A)x, f)|$ with the help of $\\| \\psi (A)x\\|$ and $\\| x\\|$. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H${\\rm{\\ddot{o}}}$rmander theorem on comparison of operators in the case when operators are acting in a Hilbert space and are functions of a self-adjoint operator. As another application we obtain Taikov-type inequalities for functions of the operator $\\frac1i \\frac {d}{dt}$ in the spaces $L_2(\\RR)$ and $L_2(\\TT)$, as well as for integrals with respect to spectral measures, defined with the help of classical orthogonal polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-11T23:53:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "47A63",
      "26D10",
      "47A63",
      "41A17",
      "47A58"
    ],
    "keywords": [
      "self-adjoint operator",
      "hilbert space",
      "taikov-type inequalities",
      "stechkins problem",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}