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  3. Operator Methods for Boundary Value Problems
  • Cited by 5
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2012
      October 2012
      ISBN:
      9781139135061
      9781107606111
      DOI:
      https://doi.org/10.1017/CBO9781139135061
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.45kg, 309 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
      Series:
      London Mathematical Society Lecture Note Series (404)
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
    Series:
    London Mathematical Society Lecture Note Series (404)
    Information

    Book description

    Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.

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