Skip to main content
  • Book
  • Open Access
  • © 2020

Boundary Value Problems, Weyl Functions, and Differential Operators

Birkhäuser
  • Self-contained and written in an accessible style

  • Provides an overview of the theory of boundary triplet techniques

Part of the book series: Monographs in Mathematics (MMA, volume 108)

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
  2. Introduction

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 1-10Open Access
  3. Linear Relations in Hilbert Spaces

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 11-106Open Access
  4. Boundary Triplets and Weyl Functions

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 107-167Open Access
  5. Spectra, Simple Operators, and Weyl Functions

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 169-221Open Access
  6. Operator Models for Nevanlinna Functions

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 223-279Open Access
  7. Boundary Triplets and Boundary Pairs for Semibounded Relations

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 281-364Open Access
  8. Sturm-Liouville Operators

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 365-498Open Access
  9. Canonical Systems of Differential Equations

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 499-576Open Access
  10. Schrödinger Operators on Bounded Domains

    • Jussi Behrndt, Seppo Hassi, Henk De Snoo
    Pages 577-630Open Access
  11. Back Matter

    Pages 631-772

About this book

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map.

The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.


Keywords

  • boundary value problem
  • selfadjoint operator
  • spectral theory
  • Weyl function
  • differential operator
  • open access
  • ordinary differential equations
  • partial differential equations

Reviews

“This monograph is a comprehensive tour de force on the theory of boundary triplets and their Weyl functions … with an eye on applications to boundary value problems for differential equations. … The bibliography is extensive (784 entries); the connection of each reference to the topics discussed in the text is elaborated in the supplementary notes at the end of each chapter. The book is very well written and carefully crafted; the exposition is amenable … .” (Julio H. Toloza, Mathematical Reviews, April, 2022)

Authors and Affiliations

  • Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

    Jussi Behrndt

  • Mathematics and Statistics, University of Vaasa, Vaasa, Finland

    Seppo Hassi

  • Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands

    Henk de Snoo

Bibliographic Information

  • Book Title: Boundary Value Problems, Weyl Functions, and Differential Operators

  • Authors: Jussi Behrndt, Seppo Hassi, Henk de Snoo

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-36714-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2020

  • License: CC BY

  • Hardcover ISBN: 978-3-030-36713-8

  • Softcover ISBN: 978-3-030-36716-9

  • eBook ISBN: 978-3-030-36714-5

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: IX, 772

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Operator Theory, Differential Equations, Systems Theory, Control

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)