It is proved that if a series with respect to the characters of abelian compact zero-dimensional group is convergent everywhere except, possibly, a countable number of points, then the coefficients of this series can be recovered from its sum by generalized Fourier formulas in which a Henstock-Kurzweil type integral is used.
VA SKVORTSOV, TULONE F (2006). On the problem of recovering the coefficients of series with respect to characters of zero-dimensional groups. TATRA MOUNTAINS MATHEMATICAL PUBLICATIONS, 34, no. 2, 307-320.
On the problem of recovering the coefficients of series with respect to characters of zero-dimensional groups
TULONE, Francesco
2006
Abstract
It is proved that if a series with respect to the characters of abelian compact zero-dimensional group is convergent everywhere except, possibly, a countable number of points, then the coefficients of this series can be recovered from its sum by generalized Fourier formulas in which a Henstock-Kurzweil type integral is used.
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