The discrete spectrum of perturbed selfadjoint operators under non-signdefinite perturbations with a large coupling constant

Given two selfadjoint operators A and V=V_+-V_-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let #alpha#>0 and let #lambda# be a regular point for A. We consider the quantity N(#lambda#, A, W_+, W_-, #alpha#) defined as the difference between the number of the eigenvalues of A(t) that pass point #lambda# from the right to the left and the number of the eigenvalues passing #lambda# from the left to the right as t increases from 0 to #alpha#>0. We study asymptotic characteristics of N(#lambda#, A, W_+, W_-, #alpha#) as #alpha##->##infinity#. Applications to Schroedinger and Dirac operators are given. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(387) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman