Operator Methods for Boundary Value Problems (repost)
Operator Methods for Boundary Value Problems (London Mathematical Society Lecture Note Series) by Professor Seppo Hassi, Professor Hendrik S. V. de Snoo and Professor Franciszek Hugon Szafraniec
English | 2012 | ISBN: 110760611X | 309 pages | PDF | 1,5 MB
English | 2012 | ISBN: 110760611X | 309 pages | PDF | 1,5 MB
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.