Schmüdgen, Konrad.

Unbounded Self-adjoint Operators on Hilbert Space [electronic resource] / by Konrad Schmüdgen. - XX, 432 p. 2 illus. online resource. - Graduate Texts in Mathematics, 265 0072-5285 ; .

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.

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


Functional analysis.
Operator theory.
Mathematical physics.
Functional Analysis.
Mathematical Methods in Physics.
Operator Theory.
Mathematical Physics.
Theoretical, Mathematical and Computational Physics.



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