Uniformly bounded Riesz bases and equiconvergence theorems

Abstract

We review some classical results on the convergence of classical trigonometric and polynomial Fourier series. Then we present a not well-known short proof of the local uniform boundedness of many classical orthonormal systems. Finally, we formulate a strong generalization of Haar's classical equiconvergence theorem.

Keywords

• Fourier Series
• Riesz basis
• classical orthogonal polynomials.