Asymptotic Formulas for Spectral and Weyl Functions of Sturm-Liouville Operators With Smooth Coefficients

Abstract

The exact asymptotic formulas are proved for the Weyl functions and spectral functions of Sturm-Liouville operators with smooth coefficients Let l be the differential operation where q is a real continuous potential. For τ = tan α we denote a selfadjoint extension in L 2 (ℝy±) of the symmetric operator defined by l, whose domain contains the set of smooth functions with compact support in ℝy±, satisfying the boundary condition Further on we shall deal only with the boundary conditions y′(0) = 0 or y(0) = 0 and corresponding operators