Unbounded Self-adjoint Operators on Hilbert Space

• Main Author: Schmüdgen, Konrad (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2012.
• Series: Graduate Texts in Mathematics, 265
• Subjects: Mathematics.; Functional analysis.; Operator theory.; Mathematical physics.; Physics.; Functional Analysis.; Mathematical Methods in Physics.; Operator Theory.; Mathematical Physics.; Theoretical, Mathematical and Computational Physics.

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 proble...

Table of Contents:

• 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.