Operator Methods for Boundary Value Problems

Operator Methods for Boundary Value Problems

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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.where stands for the time derivative of x(att= 0 this is the rightsided derivativeofxat zero). The closure of the set of ... Moreover, Ip= is a state/signal node (s/snode)ifV hasthe following properties in addition to being closed: 1. The generatinganbsp;...

Title:Operator Methods for Boundary Value Problems
Author:Seppo Hassi, Hendrik S. V. de Snoo, Franciszek Hugon Szafraniec
Publisher:Cambridge University Press - 2012-10-11


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