Uniform, on the Real Line, Equiconvergence of Spectral Expansions for the Higher-Order Differential Operators

Abstract

Result on the uniform, over the entire real line, equiconvergence of spectral expansions related to the self-adjoint extension of a general differential operation of any even order with coefficients from the one-dimensional Kato class, with the Fourier integral expansion is presented. The statement is based on the obtained uniform estimates for the spectral function of this operator.