Operator methods for boundary value problems /
edited by Seppo Hassi, Hendrik S.V. de Snoo and Franciszek Hugon Szafraniec.
- Cambridge : Cambridge University Press, 2012.
- 1 online resource (xii, 298 pages) : digital, PDF file(s).
- London Mathematical Society lecture note series ; 404 .
- London Mathematical Society lecture note series ; 404. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
1. John Williams Calkin: a short biography / S. Hassi, H.S.V. de Snoo and F.H. Szafraniec -- 2. On Calkin's abstract symmetric boundary conditions / S. Hassi and H.L. Wietsma -- 3. Boundary triplets and maximal accretive extensions of sectorial operators / Y. Arlinskiĭ -- 4. Boundary control state/signal systems and boundary triplets / D.Z. Arov, M. Kurula and O.J. Staffans -- 5. Passive state/signal systems and conservative boundary relations / D.Z. Arov, M. Kurula and O.J. Staffans -- 6. Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples / J. Behrndt and M. Langer -- 7. Boundary triplets and Weyl functions. Recent developments / V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo -- 8. Extension theory for elliptic partial differential operators with pseudodifferential methods / G. Grubb -- 9. Dirac structures and boundary relations / S. Hassi, A.J. van der Schaft, H.S.V. de Snoo and H.J. Zwart -- 10. Naĭmark dilations and Naĭmark extensions in favour of moment problems / F.H. Szafraniec.
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.