An Lp estimate for the difference of derivatives of spectral expansions arising by one-dimensional schrodinger operators

Abstract

We prove the estimate (formula), where 2 LT = p LT bes and sigma(x,f),sigma'(x,f) are the partial sums of spectral expansions of a function f(x)cBV(G), corresponding to arbitrary non-negative self-adjoint extensions of the operators Cmi=-u''+q(x)u, Cu= -u" + q(x)u (xcG) respectively; the operators are defined on an arbitrary bounded interval G C R.