Introduction to the Spectral Theory of Polynomial Operator Pencils

Author: A. S. Markus

Publisher: American Mathematical Soc.

ISBN: 0821890824

Category: Polynomial operator pencils

Page: 250

View: 7819

This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.
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Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications

Author: Manfred Möller,Vyacheslav Pivovarchik

Publisher: Birkhäuser

ISBN: 3319170708

Category: Mathematics

Page: 412

View: 4462

The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader’s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.
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Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

Author: Vladimir Kozlov,Vladimir Maz'ya

Publisher: Springer Science & Business Media

ISBN: 3662115557

Category: Mathematics

Page: 444

View: 7287

The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.
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Recent Advances in Matrix and Operator Theory

Author: Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak

Publisher: Springer Science & Business Media

ISBN: 9783764385392

Category: Mathematics

Page: 340

View: 4177

This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.
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Reproducing Kernel Spaces and Applications

Author: Daniel Alpay

Publisher: Springer Science & Business Media

ISBN: 9783764300685

Category: Mathematics

Page: 344

View: 6028

The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
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Research Paper

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1805

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Geometry & Topology

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: N.A

View: 6234

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.
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Proceedings

Mathematical, physical, and engineering sciences

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 3806

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Books in Print

Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4909

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.
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Reviews in operator theory, 1980-86

as printed in Mathematical reviews

Author: American mathematical society

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 2328

View: 4922

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Dirac-Operatoren in der Riemannschen Geometrie

Mit einem Ausblick auf die Seiberg-Witten-Theorie

Author: Thomas Friedrich

Publisher: Springer-Verlag

ISBN: 3322803023

Category: Mathematics

Page: 207

View: 1455

Dieses Buch entstand nach einer einsemestrigen Vorlesung an der Humboldt-Universität Berlin im Studienjahr 1996/ 97 und ist eine Einführung in die Theorie der Spinoren und Dirac-Operatoren über Riemannschen Mannigfaltigkeiten. Vom Leser werden nur die grundlegenden Kenntnisse der Algebra und Geometrie im Umfang von zwei bis drei Jahren eines Mathematik- oder Physikstudiums erwartet. Ein Anhang gibt eine Einführung in das aktuelle Gebiet der Seiberg-Witten-Theorie.
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Einführung in die Mechanik und Symmetrie

Eine grundlegende Darstellung klassischer mechanischer Systeme

Author: Jerrold E. Marsden,Tudor S. Ratiu

Publisher: Springer-Verlag

ISBN: 3642568599

Category: Mathematics

Page: 598

View: 6534

Symmetrie spielt in der Mechanik eine große Rolle. Dieses Buch beschreibt die Entwicklung zugrunde liegender Theorien. Besonderes Gewicht wird der Symmetrie beigemessen. Ursache hierfür sind Entwicklungen im Bereich dynamischer Systeme, der Einsatz geometrischer Verfahren und neue Anwendungen. Dieses Lehrbuch stellt Grundlagen bereit und beschreibt zahlreiche spezifische Anwendungen. Interessant für Physiker und Ingenieure. Ausgewählte Beispiele, Anwendungen, aktuelle Verfahren/Techniken veranschaulichen die Theorie.
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