Overview

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

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9789400747524

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Reviews

From the reviews: The book is devoted to the exposition of the theory of unbounded operators in the Hilbert space. ... book starts with a standard introduction to the theory of closed and closable operators, with an explanation of the important difference between self-adjoint and symmetric operators. ... Among the advantages of the book is the inclusion of a nice and voluminous selection of exercises. ... the book can be used for teaching a graduate course in spectral theory to students in analysis and to physicists ... . (G. V. Rozenblum, Mathematical Reviews, January, 2013)

From the reviews: The book is devoted to the exposition of the theory of unbounded operators in the Hilbert space. ... book starts with a standard introduction to the theory of closed and closable operators, with an explanation of the important difference between self-adjoint and symmetric operators. ... Among the advantages of the book is the inclusion of a nice and voluminous selection of exercises. ... the book can be used for teaching a graduate course in spectral theory to students in analysis and to physicists ... . (G. V. Rozenblum, Mathematical Reviews, January, 2013) The book can be used for teaching a graduate course in spectral theory to students and is also suitable for self-study. The book consists of six parts, each of which is subdivided into several chapters, each chapter ending with a section containing exercises. ... The book concludes with appendices devoted to basic topics in analysis and the theory of bounded operators. (Michael Perelmuter, Zentralblatt MATH, Vol. 1257, 2013)

Author Information

"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""."

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