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Abstrak :
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, and self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension.

Abstrak :
This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.