FREDHOLM ANALYTIC THEOREM ON THE BOUNDARY OF A DOMAIN AND ITS APPLICATION TO PERTURBATION THEORY


SERGEY NABOKO

naboko@felix.math.uab.edu

Department of Mathematical Physics
Institute for Physics
St Petersburg State University
Ulyanovskaya 1
St Petersburg 198904, Russia






The Fredholm Analytic Theorem is a standard instrument of the spectral analysis having numerous applications. Its main field is the perturbation of the discrete spectra. For the purpouses of the continuous spectra perturbation ( say in scattering theory) one needs to apply a version of the Fredholm Analytic Theorem where the invertibility is investigated on the boundary of a domain ( for example on the real axis in case of the upper half-plane). We present some ``boundary'' version of the theorem. Applications to the scattering theory are considered.


EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts