Monographs in Mathematics
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Boundary Value Problems, Weyl Functions, and Differential Operators

Authors: Behrndt, Jussi, Hassi, Seppo, de Snoo, Hendrik

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  • Open AccessSelf-contained and written in an accessible style
  • Provides an overview of the theory of boundary triplet techniques
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  • ISBN 978-3-030-36714-5
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
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Softcover $59.99
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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.


Table of contents (9 chapters)

Table of contents (9 chapters)
  • Introduction

    Pages 1-10

    Behrndt, Jussi (et al.)

  • Linear Relations in Hilbert Spaces

    Pages 11-106

    Behrndt, Jussi (et al.)

  • Boundary Triplets and Weyl Functions

    Pages 107-167

    Behrndt, Jussi (et al.)

  • Spectra, Simple Operators, and Weyl Functions

    Pages 169-221

    Behrndt, Jussi (et al.)

  • Operator Models for Nevanlinna Functions

    Pages 223-279

    Behrndt, Jussi (et al.)

Buy this book

eBook  
  • ISBN 978-3-030-36714-5
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
price for USA in USD
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Boundary Value Problems, Weyl Functions, and Differential Operators
Authors
Series Title
Monographs in Mathematics
Series Volume
108
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s)
eBook ISBN
978-3-030-36714-5
DOI
10.1007/978-3-030-36714-5
Hardcover ISBN
978-3-030-36713-8
Softcover ISBN
978-3-030-36716-9
Series ISSN
1017-0480
Edition Number
1
Number of Pages
IX, 772
Number of Illustrations
1 b/w illustrations
Topics