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Operator Theory: Advances and Applications

Complete Second Order Linear Differential Equations in Hilbert Spaces

Authors: Shklyar, Alexander Ya.

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About this book

Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.

Table of contents (13 chapters)

Table of contents (13 chapters)
  • Introduction

    Pages 1-1

    Shklyar, Alexander Ya.

  • Joint spectrum of commuting normal operators and its position. Estimates for roots of second order polynomials. Definition of well-posedness of boundary-value problems

    Pages 5-16

    Shklyar, Alexander Ya.

  • Well-posedness of boundary-value problems for equation (1) in the case of commuting self-adjoint A and B

    Pages 17-33

    Shklyar, Alexander Ya.

  • The Cauchy problem

    Pages 35-54

    Shklyar, Alexander Ya.

  • Boundary-value problems on a finite segment

    Pages 55-74

    Shklyar, Alexander Ya.

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-0348-9187-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-7643-5377-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-0348-9940-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Complete Second Order Linear Differential Equations in Hilbert Spaces
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
92
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-9187-5
DOI
10.1007/978-3-0348-9187-5
Hardcover ISBN
978-3-7643-5377-3
Softcover ISBN
978-3-0348-9940-6
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XII, 220
Topics