International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 1, Pages 25-40
doi:10.1155/S0161171201011668
Description of the structure of singular spectrum for Friedrichs model operator near singular point
Departamento de Matematicas, Universidad Simon Bolivar, Apartado Postal 89000, Caracas 1080-A, Venezuela
Received 28 January 2001
Copyright © 2001 Serguei I. Iakovlev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary part M(λ). We prove a uniqueness theorem for such a class of analytic functions.
Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular
spectrum.