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Spectral properties of Schroedinger operators and scattering theory

Publications of the Scuola Normale Superiore

By (author) Shmuel Agmon
Format: Paperback
Publisher: Birkhauser Verlag AG, Pisa, Italy
Imprint: Scuola Normale Superiore
Published: 1st Oct 1975
Dimensions: w 170mm h 240mm
ISBN-10: 8876422471
ISBN-13: 9788876422478
Barcode No: 9788876422478
These are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. We propose to discuss here certain spectral properties of Schroedinger operators H=-D+V(x) (D the Laplacian and V a potential) which have application to scattering theory. We consider an operator H with potential V of class SR. We show that the positive point spectrum of H is a discrete set in R+. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly. This property is shown to hold also for generalized eigenfunctions. We then establish the limiting absorbing principle, which is a basic tool in our study.

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