On the convergence of eigenfunction expansion in the norm of Soboleff spaces

Abstract

holds, for some z~0 . Consider the Schr6dinger operator Lo=-A+q(x ) . , D(Lo)=C~(R" ). Such operators occur as the Hamiltonian of molecules [6--12]. E.g., in the case of Li (or H~) molecule we have n=6 , m=3 , xER 3, yER 3, q(x~y)=cllx[-l+c~Iy[-~+ +ca[x-y1-1, H = A +q(x, y).. In the case of homogeneous and isotropic space the manifolds S~ are subspaces in R". It is easy to see that for dim S<=n-3 we have ~ " qELlo~(R ) if z<3/2. Indeed, taking into account