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M.G. Krein's Lectures on Entire Operators

Author: M L Gorbachuk; V I Gorbachuk
Publisher: Basel : Birkhäuser Basel : Imprint : Birkhäuser, 1997.
Series: Operator theory, advances and applications, 97.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is devoted to the theory of entire operators, founded one of the century's best known mathematicians, M.G. Krein. The theory lies at the junction of the spectral theory of Hermitian operators and the theory of analytic functions, harmoniously combining the methods of each. The purpose of the book is to show how various problems of classical and modern analysis can be looked at from the entire operator  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M L Gorbachuk; V I Gorbachuk
ISBN: 9783034889025 303488902X
OCLC Number: 851828527
Description: 1 online resource (ix, 222 pages).
Contents: 1 Some aspects of operator theory and the theory of analytic functions --
1 On spectral functions of Hermitian operators --
2. Representation of a simple Hermitian operator whose deficiency index is (1,1) --
3. On the spectrum of self-adjoint extensions of a Hermitian operator whose deficiency index is (1,1) --
4. Some aspects of the theory of analytic functions --
2 Entire operators whose deficiency index is (1,1) --
1. Quasiregular gauge --
2. Principal theorem on regular points of fM(z) --
3. u -regular points of a Hermitian operator --
4. Functions e(z) and?M(Z) --
5. Entire operators --
6. R-functions and generalized resolvents of a Hermitian operator --
7. On distribution functions of a Hermitian operator --
8. Method of directing functionals --
9. Operator, entire with respect to a generalized gauge --
3 Applications of entire operator theory to some classical problems of analysis --
1. Power moment problem --
2. Continuation problem for positive definite functions --
3. Unitary and spiral curves --
Appendix 1 On entire operators whose defect numbers are arbitrary --
Appendix 2 Enture operators represented by differential operators --
Appendix 3 On a difficult problem of operator theory and its relation to classical analysis --
Comments.
Series Title: Operator theory, advances and applications, 97.
Responsibility: by M.L. Gorbachuk, V.I. Gorbachuk.

Abstract:

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.

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