Operator Theory: Advances and Applications

M.G. Krein’s Lectures on Entire Operators

Editors: Gorbachuk, Myroslav (Ed.)

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About this book

This book is devoted to the theory of entire Hermitian operators, an important branch of functional analysis harmoniously combining the methods of operator theory and the theory of analytic functions. This theory anables various problems of classical and modern analysis to be looked at from a uniform point of view. In addition, it serves as a source for setting and solving many new problems in both theories. The three chapters of the book are based on the notes written by his students of M. G. Krein's lectures on the theory of entire operators with (1,1)­ deficiency index which he delivered in 1961 at the Pedagogical Institute of Odessa, and on his works on the extension theory of Hermitian operators and the theory of analytic functions. The theory is further developed in the direction of solving the problems set up by Krein at ICM-66 in the first two appendices. The first concerns the case of Hermitian operators with arbitrary defect numbers, entire with respect to an ordinary gauge and to a generalized one as well. The other focuses on the entire operators representable by differential operators. The third appendix is the translation from Russian of the unpublished notes of Krein's lecture in which, in particular, the place of the theory of entire operators in the whole analysis is elucidated. In Krein's mathematical heritage the theory of entire operators occupies a special position.

Table of contents (3 chapters)

Table of contents (3 chapters)
  • Some Aspects of Operator Theory and the Theory of Analytic Functions

    Gorbachuk, M. L. (et al.)

    Pages 1-45

  • Entire Operators whose Deficiency Index is (1,1)

    Gorbachuk, M. L. (et al.)

    Pages 47-118

  • Applications of Entire Operator Theory to Some Classical Problems of Analysis

    Gorbachuk, M. L. (et al.)

    Pages 119-160

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-0348-8902-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA in USD
  • ISBN 978-3-0348-9821-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
M.G. Krein’s Lectures on Entire Operators
Editors
  • Myroslav Gorbachuk
Series Title
Operator Theory: Advances and Applications
Series Volume
97
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8902-5
DOI
10.1007/978-3-0348-8902-5
Softcover ISBN
978-3-0348-9821-8
Series ISSN
0255-0156
Edition Number
1
Number of Pages
IX, 222
Topics