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.

About the Authors

Seppo Hassi is a Professor of Mathematics at the University of Vaasa, having previously worked at the University of Helsinki. His main research interests are in operator and spectral theory and applications in analysis and mathematical physics.

Hendrik S. V. de Snoo has worked at the University of Groningen since 1972 and obtained the title of Honorary Professor in 2010. He has been a visiting professor at the University of California, Los Angeles, Western Washington University and the University of the Witwatersrand. He recently held a Mercator professorship at the TU Berlin. He has a lifelong interest in abstract boundary value problems.

Franciszek Hugon Szafraniec has established his mathematical career within Jagiellonian University, entering it in 1957 as a student. Receiving all appropriate scientific degrees and titles and going through all the various academic positions there, he retired in 2010. He visited numerous scholarly institutions and attended a vast number of conferences, all of which enriched his main research interest: Hilbert space methods.

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