Operator Methods for Boundary Value Problems (eBook, PDF)

Redaktion: Hassi, Seppo

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 11. Oktober 2012
• Englisch
• ISBN-13: 9781139558877
• Artikelnr.: 38275710

Inhaltsangabe

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.