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Some properties of general orthonormal systems

Volume 162 / 2020

Vakhtang Tsagareishvili Colloquium Mathematicum 162 (2020), 201-209 MSC: Primary 42C10. DOI: 10.4064/cm7857-9-2019 Published online: 29 April 2020


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.


  • Vakhtang TsagareishviliFaculty of Exact and Natural Sciences
    I. Javakhishvili Tbilisi State University
    13 University St.
    Tbilisi 0186, Georgia

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