Growth of Norms in L2 of Derivatives of the Steklov Functions and Properties Defined by the Best Approximations and Fourier Coefficients

Abstract

In the paper, for periodic functions, a connection between integrals of norms in L₂ of derivatives of the Steklov functions and series constructed from Fourier coefficients and the best approximations in L₂ is established, and the question on their simultaneous convergence or divergence is examined. Similar investigations are carried out for even and odd periodic functions. Bibliography: 13 titles.