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

• Main Authors: Möller, Manfred (Author), Pivovarchik, Vyacheslav (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Series: Operator Theory: Advances and Applications, 246
• Subjects: Mathematics.; Operator theory.; Differential equations.; Mathematical physics.; Operator Theory.; Ordinary Differential Equations.; Mathematical Physics.

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,...

Table of Contents:

• 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.