Larry Gogoladze

On the Convergence of Conjugate Trigonometric Polynomials

Abstract:
Sufficient conditions are found, under which for $f\in C([-\pi,\pi])$ or $f\in L([-\pi,\pi])$ the convergence of a sequence of trigonometric polynomials in the norms of these spaces implies the convergence of their conjugates in the same norms.

Keywords:
Conjugate functions, de la Valle-Poussin means, best approximation.

MSC 2000: 42A50