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T. Akhobadze (1982)
On convergence and summability of Fourier seriesAnalysis Mathematica, 8
N. Kirchhoff, R. Nessel (1992)
Divergence almost everywhere of a pointwise comparison of trigonometric convolution processes with their discrete analoguesJournal of Approximation Theory, 70
(1994)
Fizmatgiz, Moscow, 1961
J. Approx. Theory
M. Ramanujan, N. Bary, Margaret Mullins (1966)
Treatise of Trigonometric Series
The process of Fejér type trigonometric convolution and its discrete analogue have equivalent uniform residues. The situation changes under pointwise comparison. In this direction negative results have been obtained by different authors. One result of such a type is given in the present paper. In particular, a counter-example is constructed for which both comparisons diverge on the set of complete measure. The smoothness of the counter-example as well as some other problems are investigated.
Georgian Mathematical Journal – de Gruyter
Published: Jun 1, 1995
Keywords: Sequence of convolution operators; sequence of discrete analogues of convolution operators; Fejér type kernels; pointwise comparison
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