This textbook provides a modern account of the theory of unbounded self-adjoint operators on Hilbert spaces and their spectral theory, with emphasis on applications in mathematical physics (Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm–Liouville operators, and the Hamburger moment problem). The new edition has been thoroughly revised and updated and features an extensive treatment of the self-adjoint extension theory of symmetric operators. In addition, a number of advanced special topics are presented at the textbook level, accompanied by numerous illustrative examples and exercises. The main themes of the book are:Basics of unbounded operators and fundamental self-adjointness criteriaSpectral integrals, spectral theorems, and functional calculus for self-adjoint and normal operatorsPerturbations of self-adjointness and of the spectra of self-adjoint operatorsForms and operatorsBoundary tripletsThe Krein transform and the Krein–Vishik–Birman theory of positive self-adjoint extensionsWith several updates and additions, this edition further enhances an established standard reference and accessible entry point to the subject.
