Operator Methods for Boundary Value Problems
Operator Methods for Boundary Value Problems
Hendrik S. V. de Snoo, Rijksuniversiteit Groningen, The Netherlands
Franciszek Hugon Szafraniec, Jagiellonian University, Krakow
£53.99
GBPPresented 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.
- Presents recent developments in boundary mappings for ODEs, PDEs and systems theory
- Written by leading researchers
- Covers a wide range of topics from the abstract to the applied
Product details
October 2012Paperback
9781107606111
309 pages
226 × 152 × 15 mm
0.45kg
Available
Table of Contents
- Preface
- John Williams Calkin: a short biography S. Hassi, H. S. V. de Snoo and F. H. Szafraniec
- 1. On Calkin's abstract symmetric boundary conditions S. Hassi and H. L. Wietsma
- 2. Maximal accretive extensions of sectorial operators Yu. M. Arlinskii
- 3. Boundary control state/signal systems and boundary triplets D. Z. Arov, M. Kurula and O. J. Staffans
- 4. Passive state/signal systems and conservative boundary relations D. Z. Arov, M. Kurula and O. J. Staffans
- 5. Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triplets J. Behrndt and M. Langer
- 6. Boundary triplets and Weyl functions. Recent developments V. A. Derkach, M. M. Malamud, S. Hassi and H. S. V. de Snoo
- 7. Extension theory for elliptic partial differential operators with pseudodifferential methods G. Grubb
- 8. Dirac structures and boundary relations S. Hassi, A. J. Van der Schaft, H. S. V. de Snoo and H. Zwart
- 9. Naimark dilations and Naimark extensions in favour of moment problems F. H. Szafraniec.
