On bounds for Titchmarsh–Weyl m-coefficients and for spectral functions for second-order differential operators

Abstract

SynopsisOrder-of-magnitude results are extended to the case of general second-order term, with coefficient not necessarily of fixed sign, with general positive weight-function. The bounds are used to establish the expression for the Titchmarsh–Weyl function m(λ) as a Nevanlinna function in terms of the spectral function.