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Recent Advances in Operator Theory in Hilbert and Krein Spaces

Part of the Operator Theory: Advances and Applications Book Series (volume 198)

Editors: Behrndt, Jussi; Förster, Karl-Heinz; Trunk, Carsten

DOI: 10.1007/978-3-0346-0180-1

ISBN: 978-3-0346-0179-5

Publisher: Birkhäuser Basel - Springer Journals

Jan 9, 2010

1 - 10 of 17 Chapters

LitStream

Chapter 1Local Scattering Problem and a Solvable Model of Quantum Network

Adamyan, Vadym; Pavlov, Boris

Pages: 1 –10

[A local scattering theory on finite spectral interval for pairs of selfadjoint operators, which are different extensions of the same densely definite symmetric operator, is developed. The present investigation was motivated by scattering problems for Schrödinger operators modeling the energy...
LitStream

Chapter 2Quadratic (Weakly) Hyperbolic Matrix Polynomials: Direct and Inverse Spectral Problems

Azizov, T. Ya.; Dijksma, A.; Förster, K.-H.; Jonas, P.

Pages: 11 –40

[Let L be a monic quadratic weakly hyperbolic or hyperbolic n × n matrix polynomial. We solve some direct spectral problems: We prove that the eigenvalues of a compression of L to an (n − 1)-dimensional subspace of ℂn block-interlace and that the eigenvalues of a one-dimensional perturbation of L...
LitStream

Chapter 3A Theorem on Existence of Invariant Subspaces for J-binoncontractive Operators

Azizov, Tomas Ya.; Khatskevich, Victor A.

Pages: 41 –48

[Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{H}...
LitStream

Chapter 4Moment Problems for Real Measures on the Unit Circle

Bakonyi, Mihály; Lopushanskaya, Ekaterina V.

Pages: 49 –60

[Given a sequence (tj)jn=−n of complex numbers such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 5Finite Rank Perturbations, Scattering Matrices and Inverse Problems

Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen

Pages: 61 –85

[In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite-dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets...
LitStream

Chapter 6Conditions for an Indefinite Sturm-Liouville Riesz Basis Property

Binding, Paul; Fleige, Andreas

Pages: 87 –95

[We consider the Sturm-Liouville problem −y″ = λry on [−1, 1] with Dirichlet boundary conditions and with an indefinite weight function r which changes sign at 0. We discuss several conditions known to be either necessary or sufficient for the eigenfunctions to form a Riesz basis of the Hilbert...
LitStream

Chapter 7Convergence of Diagonal Padé Approximants for a Class of Definitizable Functions

Derevyagin, Maxim; Derkach, Vladimir

Pages: 97 –124

[Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 8Approximation of Nκ∞-functions II: Convergence of Models

Dijksma, Aad; Luger, Annemarie; Shondin, Yuri

Pages: 125 –169

[This paper is a continuation of Part I, au][9]_in the list of references, where models for Nк∞-functions have been studied in detail. In the present paper we investigate the convergence of the corresponding models as a singular Nк∞ -function is approximated by regular Nк∞-functions. This...
LitStream

Chapter 9Nonnegative Extensions via Embeddings

Förster, K.-H.; Nafalska, M. M.

Pages: 171 –183

[For a given densely defined nonnegative operator in a Hilbert space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 10Fredholm Properties of Unbounded Operators on Interpolation Spaces

Günther, Kerstin

Pages: 185 –210

[We study Fredholm properties and properties on the continuous invertibility of unbounded operators S0, S1, S△ and SΣ, which are connected to a linear operator between compatible couples. If S0 and S1 are everywhere defined and bounded, then we obtain the operators usually considered in the...

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