Operator Methods for Boundary Value Problems

A collection of articles on operator-theoretic methods for boundary-value problems. Contains recent developments that will appeal to researchers and students.

Seppo Hassi (Edited by), Hendrik S. V. de Snoo (Edited by), Franciszek Hugon Szafraniec (Edited by)

9781107606111, Cambridge University Press

Paperback / softback, published 11 October 2012

309 pages
22.6 x 15.2 x 1.5 cm, 0.45 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ]