Unbounded Self-adjoint Operators on Hilbert Space

Buch | Hardcover
432 Seiten
2012
Springer (Verlag)
978-94-007-4752-4 (ISBN)

Lese- und Medienproben

Unbounded Self-adjoint Operators on Hilbert Space - Konrad Schmüdgen
90,94 inkl. MwSt
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) .
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger  operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics   are treated on a text book level  accompanied by numerous illustrating examples and exercises. The main themes of the book are the following:
- Spectral integrals and  spectral decompositions of self-adjoint and normal operators
- Perturbations of self-adjointness and of spectra of self-adjoint operators
- Forms and operators
- Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension

Schmuedgen is professor at the Mathematics Department of the University of Leipzig. Prof. Pavel Exner wrote about him: "In the eighties he was regarded at the Leipzig University as a rising star and the most gifted in the mathematical physics group".

I Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral Integrals.- 5 Spectral Decomposition of Selfadjoint and Normal Operators.- III Special Topics.- 6 One-Parameter Groups and Semigroups of Operators.- 7 Miscellaneous.- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators.- 8 Perturbations of Selfadjoint Operators.- 9 Trace Class Perturbations of Spectra of Selfadjoint Operators.- V Forms and Operators.- 10 Semibounded Forms and Selfadjoint Operators.- 11 Sectorial Forms and m-Sectorial Operators.- 12 Discrete Spectrum of Selfadjoint Operators.- VI Selfadjoint Extention Theory of Symmetric Operators.- 13 Selfajoint Extensions: Cayley Transform and Krein Transform.- 14 Selfadjoint Extensions: Boundary Triplets.- 15 Sturm-Liouville Operators.- One-Dimensional Moment Problem.

Reihe/Serie Graduate Texts in Mathematics ; 265
Zusatzinfo XX, 432 p.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie
Schlagworte Banach space • Hamburger moment problem • hilbert space • Perturbation of self-adjointness • Schrödinger Operators • Self-adjoint extension theory • self-adjoint operators • spectral theory • Sturm-Liouville operators
ISBN-10 94-007-4752-7 / 9400747527
ISBN-13 978-94-007-4752-4 / 9789400747524
Zustand Neuware
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