Unbounded Self-adjoint Operators on Hilbert Space

Graduate Texts in Mathematics #265

by Konrad Schmüdgen

This book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with emphasis on applications in mathematical physics (especially, Schrodinger operators) and analysis (Dirichlet and Neumann LaPlacians, Sturm-Liouville operators, Hamburger moment problems). 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 spectra of self-adjoint operators
-Forms and operators
-Self-adjoint extension theory: boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extensions.

452 pages, Hardcover

First published July 7, 2012

Reviews

[Alexandros Kazantzidis · Rating 5 out of 5]

Haven't read all of it, but I have read big chunks of it, including the first six chapters in their entirety.

It is extremely well-written, proofs are very easy to follow - even the most technical ones - , there's plenty of examples and exercises, the exposition on the unbounded functional calculus is fantastic, pretty much all of the fundamental "big theorems" of the field seem to have been included...


Extremely highly recommended, both as a textbook, and as a reference.