Description

Book Synopsis
The work on the foundations of Quantum Mechanics in the 1920s and 1930s provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic has developed in several directions. This book summarizes some of these directions.

Table of Contents
  • Differential equations and expressions: First order systems
  • Quasi-differential expressions and equations
  • The Lagrange identity and maximal and minimal operators
  • Deficiency indices
  • Symmetric, self-adjoint, and dissipative operators: Regular symmetric operators
  • Singular symmetric operators
  • Self-adjoint operators
  • Self-adjoint and symmetric boundary conditions
  • Solutions and spectrum
  • Coefficients, the deficiency index, spectrum
  • Dissipative operators
  • Two-interval problems: Two-interval symmetric domains
  • Two-interval symmetric domain characterization with maximal domain functions
  • Other topics: Green's function and adjoint problems
  • Notation
  • Topics not covered and open problems
  • Bibliography
  • Index.

    Ordinary Differential Operators

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      A Hardback by Aiping Wang, Anton Zettl

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 12/30/2019 12:00:00 AM
        ISBN13: 9781470453664, 978-1470453664
        ISBN10: 1470453665

        Description

        Book Synopsis
        The work on the foundations of Quantum Mechanics in the 1920s and 1930s provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic has developed in several directions. This book summarizes some of these directions.

        Table of Contents
        • Differential equations and expressions: First order systems
        • Quasi-differential expressions and equations
        • The Lagrange identity and maximal and minimal operators
        • Deficiency indices
        • Symmetric, self-adjoint, and dissipative operators: Regular symmetric operators
        • Singular symmetric operators
        • Self-adjoint operators
        • Self-adjoint and symmetric boundary conditions
        • Solutions and spectrum
        • Coefficients, the deficiency index, spectrum
        • Dissipative operators
        • Two-interval problems: Two-interval symmetric domains
        • Two-interval symmetric domain characterization with maximal domain functions
        • Other topics: Green's function and adjoint problems
        • Notation
        • Topics not covered and open problems
        • Bibliography
        • Index.

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