Divergent Fourier series of integrable functions with respect to orthonormal systems

A. S. Krantsberg

Moscow Institute of Municipal Economy and Construction

Abstract: There exist two orthonormal systems such that the Fourier series of each function $f\in L[0,1]$, $f\ne0$, with respect to at least one of these systems diverges on a set of positive measure.

UDC: 517

Received: 25.11.1996
Revised: 03.09.1997

DOI: 10.4213/mzm1338

 English version: Mathematical Notes, 1998, 63:5, 631–637

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