Some properties of general orthonormal systems
Volume 162 / 2020
Colloquium Mathematicum 162 (2020), 201-209
MSC: Primary 42C10.
DOI: 10.4064/cm7857-9-2019
Published online: 29 April 2020
Abstract
We investigate the convergence of a special series involving the Fourier coefficients of function of bounded variation with respect to general orthonormal systems (ONS). We find a condition for the functions of an ONS under which the special series is convergent for any function of bounded variation and for any orthonormal system. The results obtained demonstrate the differences between the properties of classical ONS (trigonometric, Haar, Walsh) and the case of general ONS.
