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This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.

Operator theory. --- Indefinite inner product spaces. --- Kreĭn spaces.

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This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike.

Functions of several complex variables. --- Analytic spaces. --- Indefinite inner product spaces. --- Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Indefinite scalar product spaces --- Inner product spaces, Indefinite --- Scalar product spaces, Indefinite --- Spaces with indefinite inner product --- Inner product spaces --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Complex variables --- Several complex variables, Functions of --- Functions of complex variables --- Operator theory. --- Matrix theory. --- Differential Equations. --- Operator Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Analytic spaces --- Indefinite inner product spaces --- Algebras, Linear --- Algebra. --- Differential equations. --- Mathematics

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This volume contains 16 original research papers written by participants of the 3rd Workshop on Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems, which was held at the Technische Universität Berlin, Germany, December 12–14, 2003. They deal with spectral and perturbation theory of linear operators in indefinite inner product spaces and their applications. The topics include extension theory of symmetric operators, normal operators, realization theory and models of generalized Nevanlinna functions, interpolation problems, reproducing kernel spaces, matrix and operator pencils, locally definitizable functions, and semigroups.

Operator theory --- Kreĭn spaces --- Eigenvalues --- Matrices --- J-spaces --- Spaces, J --- -Spaces, Kreĭn --- Indefinite inner product spaces --- Operator theory. --- Integral Transforms. --- Mathematical physics. --- Functional analysis. --- Operator Theory. --- Integral Transforms, Operational Calculus. --- Mathematical Methods in Physics. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Physics --- Transform calculus --- Transformations (Mathematics) --- Functional analysis --- Mathematics --- Integral transforms. --- Operational calculus. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Operational calculus --- Differential equations --- Electric circuits --- Krein spaces