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Author: I. Gohberg Publisher: Birkhäuser ISBN: 3034891067 Category : Mathematics Languages : en Pages : 327
Book Description
The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.
Author: I. Gohberg Publisher: Birkhäuser ISBN: 3034891067 Category : Mathematics Languages : en Pages : 327
Book Description
The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.
Author: Hans Volkmer Publisher: Springer ISBN: 3540460152 Category : Mathematics Languages : en Pages : 164
Book Description
This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.
Author: Alexander G. Ramm Publisher: American Mathematical Soc. ISBN: 0821819909 Category : Mathematics Languages : en Pages : 594
Book Description
Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.
Author: Jussi Behrndt Publisher: Springer Nature ISBN: 3030367142 Category : Mathematics Languages : en Pages : 772
Book Description
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Author: Seppo Hassi Publisher: Cambridge University Press ISBN: 1139561316 Category : Mathematics Languages : en Pages : 297
Book Description
Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.
Author: Alexander Andreevych Boichuk Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110378442 Category : Mathematics Languages : en Pages : 314
Book Description
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time. With the help of the technique of generalized inverse operators, the Vishik– Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction. For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers. For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents: Preliminary Information Generalized Inverse Operators in Banach Spaces Pseudoinverse Operators in Hilbert Spaces Boundary-Value Problems for Operator Equations Boundary-Value Problems for Systems of Ordinary Differential Equations Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations Solutions of Differential and Difference Systems Bounded on the Entire Real Axis
Author: Karl-Heinz Förster Publisher: Springer Science & Business Media ISBN: 3764374535 Category : Mathematics Languages : en Pages : 307
Book Description
This volume contains a collection of recent original research papers in operator theory in Krein spaces, on generalized Nevanlinna functions, which are closely connected with this theory, and on nonlinear eigenvalue problems. Key topics include: spectral theory for normal operators; perturbation theory for self-adjoint operators in Krein spaces; and, models for generalized Nevanlinna functions.
Author: Donal O'Regan Publisher: World Scientific ISBN: 9810217609 Category : Mathematics Languages : en Pages : 173
Book Description
This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems. It also provides a detailed account of the current state of the literature on existence theory for ordinary differential equations. Results are presented for finite and semi-infinite intervals. Singularities in both independent and dependent variables are discussed.
Author: Sergei G. Pyatkov Publisher: Walter de Gruyter ISBN: 3110900165 Category : Mathematics Languages : en Pages : 364
Book Description
This monograph describes mathematical methods applicable to studying nonclassical problems of mathematical physics. The emphasis of the book is on applications of the interpolar theory of Banach spaces to the theory of linear operators to be expotentially dichotomous, to some continuity properties of linear operators in Hilbert scales, to the Riesz basis property of eigenelements and associated elements of linear pencils and the correspondending elliptic problems with indefinite weight functions, and to studying nonclassical boundary value problems for first order operator-differential equations.
Author: I. Gohberg
Author: I. Gohberg
Author: Israel Gohberg
Author: Hans Volkmer
Author: Alexander G. Ramm
Author: Jussi Behrndt
Author: Seppo Hassi
Author: Alexander Andreevych Boichuk
Author: Karl-Heinz Förster
Author: Donal O'Regan
Author: Sergei G. Pyatkov