rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Sturm-Liouville operators, their spectral theory, and some applications
  name:
    name part: Gesztesy, Fritz
    name part: 1953-
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Nichols, Roger (Roger Allen)
    name part: 1984-
    role:
      role term: author.
  name:
    name part: Zinchenko, Maxim
    name part: 1980-
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: riu
    date issued: 2024
    copyright date: 2024
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xv, 927 pages ; 27 cm.
  abstract: This book provides a detailed treatment of the various facets of modern Sturm-Liouville theory, including such topics as Weyl-Titchmarsh theory, classical, renormalized and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm-Liouville operators, strongly singular Sturm-Liouville differential operators, generalized boundary values and Sturm-Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin-Yuditskii class, as well as a detailed collection of singular examples, such as the Bessed, generalized Bessed and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten-von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein-von Neumann entensions, boundary triplets for ODEs, Krein-type resolvent formulas, sequilinear forms, Nevanlinna-Herglotz functions and Bessed funsctions.
  table of contents: Introduction -- A bit of physical motivation -- Preliminaries on ODEs -- The regular problem on a compact interval [a,b]⊂R -- The singular problem on (a,b)⊆R -- The spectral function for a problem with a regular endpoint -- The 2 x 2 spectral matrix function in the presence of two singular interval endpoints for the problem on (a,b)⊆R -- Classical oscillation theory, principal solutions, and nonprincipal solutions -- Renormalized oscillation theory -- Perturbative oscillation criteria and perturbative Hardy-type inequalities -- Boundary data maps -- Spectral zeta functions and computing traces and determinants for Sturm-Liouville operators -- The singular problem on (a,b)⊆R revisited -- Four-coefficient Sturm-Liouville operators and distributional potential coefficients -- Epilogue : applications to some partial differential equations of mathematical physics -- Appendix A. Basic facts on linear operators -- Appendix B. Basics of spectral theory -- Appendix C. Classes of bounded linear operators -- Appendix D. Extensions of symmetric operators -- Appendix E. Elements of sesquilinear forms -- Appendix F. Basics of Nevanlinna-Herglotz functions -- Appendix G. Bessel functions in a nutshell.
  note: Fritz Gesztesy, Roger Nichols, Maxim Zinchenko.
  note: Includes bibliographical references and indexes.
  subject:
    topic: Sturm-Liouville equation
  subject:
    topic: Operator theory
  subject:
    topic: Spectral theory (Mathematics)
  classification: QA372 .G47 2024
  classification: 515/.352
  classification: 34B24 34L10 47B25
  related item:
    title info:
      title: Colloquium publications (American Mathematical Society) ; v. 67
  identifier: 9781470476663
  identifier: 1470476665
  identifier: 9781470478247
  identifier: 2024020468
  record info:
    record content source: DLC
    record creation date: 240510
    record change date: 20250219165401.3
    record identifier: in00005617200