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Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution

Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution

Georgian Mathematical Journal , Volume 2 (3) – Jun 1, 1995

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References (5)

Publisher
de Gruyter
Copyright
© 1995 Plenum Publishing Corporation
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.1995.313
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Georgian Mathematical Journalde 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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