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

,

Wysyłka: Niedostępna
Sugerowana cena detaliczna 418,00 PLN
Nasza cena: 390,83 PLN
Oszczędzasz 6%
Dodaj do Schowka
Zaloguj się
Przypomnij hasło
×
×
Paypo
Oferujemy szeroki asortyment - ponad 120 tys. produktów
Dysponujemy solidną wiedzą - działamy już 11 lat
Dbamy o wybór najcenniejszych tytułów

Opis: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications - Vyacheslav Pivovarchik, Manfred Moller

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-lambdaI 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.Preface.- Part I: Operator Pencils.- 1.Quadratic Operator Pencils.- 2.Applications of Quadratic Operator Pencils.- 3.Operator Pencils with Essential Spectrum.- 4.Operator Pencils with a Gyroscopic Term.- Part II: Hermite-Biehler Functions.- 5.Generalized Hermite-Biehler Functions.- 6.Applications of Shifted Hermite-Biehler Functions.- Part III: Direct and Inverse Problems.- 7.Eigenvalue Asymptotics.- 8.Inverse Problems.- Part IV: Background Material.- 9.Spectral Dependence on a Parameter.- 10.Sobolev Spaces and Differential Operators.- 11.Analytic and Meromorphic Functions.- 12.Inverse Sturm-Liouville Problems.- Bibliography.- Index.- Index of Notation.


Szczegóły: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications - Vyacheslav Pivovarchik, Manfred Moller

Tytuł: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications
Autor: Vyacheslav Pivovarchik, Manfred Moller
Producent: Birkhauser
ISBN: 9783319170695
Rok produkcji: 2015
Ilość stron: 412
Oprawa: Twarda
Waga: 0.78 kg


Recenzje: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications - Vyacheslav Pivovarchik, Manfred Moller

Zaloguj się
Przypomnij hasło
×
×

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

,

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-lambdaI 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.Preface.- Part I: Operator Pencils.- 1.Quadratic Operator Pencils.- 2.Applications of Quadratic Operator Pencils.- 3.Operator Pencils with Essential Spectrum.- 4.Operator Pencils with a Gyroscopic Term.- Part II: Hermite-Biehler Functions.- 5.Generalized Hermite-Biehler Functions.- 6.Applications of Shifted Hermite-Biehler Functions.- Part III: Direct and Inverse Problems.- 7.Eigenvalue Asymptotics.- 8.Inverse Problems.- Part IV: Background Material.- 9.Spectral Dependence on a Parameter.- 10.Sobolev Spaces and Differential Operators.- 11.Analytic and Meromorphic Functions.- 12.Inverse Sturm-Liouville Problems.- Bibliography.- Index.- Index of Notation.

Powiadom o dostępności
Podaj swój e-mail a zostaniesz poinformowany jak tylko pozycja będzie dostępna.
×
Cena 418,00 PLN
Nasza cena 390,83 PLN
Oszczędzasz 6%
Wysyłka: Niedostępna
Dodaj do Schowka
Zaloguj się
Przypomnij hasło
×
×

Paypo

Szczegóły: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications - Vyacheslav Pivovarchik, Manfred Moller

Tytuł: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications
Autor: Vyacheslav Pivovarchik, Manfred Moller
Producent: Birkhauser
ISBN: 9783319170695
Rok produkcji: 2015
Ilość stron: 412
Oprawa: Twarda
Waga: 0.78 kg


Recenzje: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and Their Applications - Vyacheslav Pivovarchik, Manfred Moller

Zaloguj się
Przypomnij hasło
×
×

Klienci, którzy kupili oglądany produkt kupili także:


Zaloguj się
Przypomnij hasło
×
×
Dodane do koszyka
×