Operator Methods for Boundary Value Problems

By: Seppo Hassi (Editor), Hendrik S. V. de Snoo (Editor), Franciszek Hugon Szafraniec (Editor)

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Paperback | 11 October 2012

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312 Pages

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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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Science Physics Mathematical Physics Integral Calculus & Equations

Preface
John Williams Calkin: a short biography
On Calkin's abstract symmetric boundary conditions
Maximal accretive extensions of sectorial operators
Boundary control state/signal systems and boundary triplets
Passive state/signal systems and conservative boundary relations
Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triplets
Boundary triplets and Weyl functions. Recent developments
Extension theory for elliptic partial differential operators with pseudodifferential methods
Dirac structures and boundary relations
Naimark dilations and Naimark extensions in favour of moment problems
Table of Contents provided by Publisher. All Rights Reserved.

Operator Methods for Boundary Value Problems

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