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Operator methods for boundary value problems

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概要 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. Th...is 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.続きを見る
目次 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.
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登録日 2020.06.27
更新日 2020.06.28