This article is cited in 8 papers

Unbounded divergence of Fourier series of continuous functions

V. V. Buzdalin

Patrice Lumumba Peoples Friendship University

Abstract: For any given set $E\subset[0,\,2\pi)$, of measure zero, a function $f(t)\in C(0,\,2\pi)$, is constructed whose Fourier series is unboundedly divergent on $E$. If $E$ is closed, there is a function $\varphi(t)\in C(0,2\pi)$, whose Fourier series diverges unboundedly on $E$ and converges on $[0,2\pi)\setminus E$.

UDC: 517.5

Received: 05.05.1969

 English version: Mathematical Notes, 1970, 7:1, 5–12

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