Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications

de Manfred Möller
État : Neuf
134,03 €
TVA incluse - Livraison GRATUITE
Manfred Möller Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications
Manfred Möller - Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications
Manfred Möller - Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications

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Livraison : entre vendredi 29 octobre 2021 et mardi 2 novembre 2021
Vente et expédition: Dodax

La description

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.


Contributeurs

Écrivain:
Manfred Möller
Vyacheslav Pivovarchik

Détails du produit

Commentaire illustrations:
Bibliographie
Remarks:

Provides comprehensive information on the spectral properties of quadratic operator pencils


Includes a detailed discussion of applications to spectral problems from physics and engineering


Presents a thorough investigation of the connection between the spectral properties of quadratic operator pencils and generalized Hermite-Biehler functions


Many of the results presented have never before been published in a monograph

Type de média:
Couverture rigide
Éditeur:
Springer International Publishing
Évaluation:
"In this monograph the authors study spectral properties of polynomial operator pencils ... . Large number so applications is an important feature of the book, and makes it highly useful for researchers interested in diverse problem of applied mathematics. ... The book is highly readable and the presentation is mathematically rigorous." (Ivica Nakic, Mathematical Reviews, July, 2016)

Langues:
Anglais
Nombre de pages:
412

Données de base

Type d'produit:
Livre relié
Date de publication:
29 juin 2015
Dimensions du colis:
0.234 x 0.16 x 0.03 m; 0.68 kg
GTIN:
09783319170695
DUIN:
F64GRRU06CL
134,03 €
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