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**Linear operators in Hilbert spaces. Part II: Applications.
(Lineare Operatoren in Hilberträumen. Teil II: Anwendungen.)**
*(German)*
Zbl 1025.47001

Mathematische Leitfäden. Stuttgart: Teubner. 404 S. (2003).

This second volume of the textbook [for Part I, see Zbl 0972.47002] on linear operators in Hilbert spaces continues the systematic treatment of self-adjoint operators in Hilbert spaces, but the major part of the book deals with applications to differential operators relevant in mathematical physics.

Topics include the spectral decomposition of self-adjoint operators, Sturm-Liouville and Dirac operators (including an extra section on the periodic-coefficient case), one- and \(N\)-particle Schrödinger operators and scattering theory.

Due to the split of the original edition into two volumes, a fair amount of new material has been added in comparison to the original edition [Zbl 0344.47001]. Moreover, the chapter on scattering theory has been enlarged considerably as the new edition contains sections on Enß-perturbations and on multi-channel scattering.

As in the first volume, complete proofs of all results are given and there are many challenging exercises at the end of most chapters. New concepts are introduced and motivated in detail, the book is a self-cointained introduction to applications of spectral theory in Hilbert spaces. It may therefore be used as a basis for lectures as well as for graduate seminars.

Topics include the spectral decomposition of self-adjoint operators, Sturm-Liouville and Dirac operators (including an extra section on the periodic-coefficient case), one- and \(N\)-particle Schrödinger operators and scattering theory.

Due to the split of the original edition into two volumes, a fair amount of new material has been added in comparison to the original edition [Zbl 0344.47001]. Moreover, the chapter on scattering theory has been enlarged considerably as the new edition contains sections on Enß-perturbations and on multi-channel scattering.

As in the first volume, complete proofs of all results are given and there are many challenging exercises at the end of most chapters. New concepts are introduced and motivated in detail, the book is a self-cointained introduction to applications of spectral theory in Hilbert spaces. It may therefore be used as a basis for lectures as well as for graduate seminars.

Reviewer: André Noll (Darmstadt)

### MSC:

47-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory |

47N20 | Applications of operator theory to differential and integral equations |

47A10 | Spectrum, resolvent |

47B25 | Linear symmetric and selfadjoint operators (unbounded) |