Abstract:
For simple trigonometric series it is shown, in particular, that if the trigonometric series is Riemann summable in measure to an integrable function $f$ and if the Riemann majorant is finite everywhere except possibly on a countable set, then this series is the Fourier series of the function $f$. Uniqueness theorems for multiple trigonometric series are obtained on the basis of this result.
Bibliography: 14 titles.
Fulltext:
PDF file (565 kB)
