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

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