Comparison of V- and S-Dini Tests. Counterexamples for Symmetric Dini Tests with Respect to Generalized Haar and Walsh Systems

Comparison of V- and S-Dini Tests. Counterexamples for Symmetric Dini Tests with Respect to Generalized Haar and Walsh Systems

In this paper, we prove that in symmetric Dini tests with respect to Price and generalized Haar systems both conditions are essential; no one of them alone guarantees the convergence of the Fourier series independently of the majorant of Dirichlet kernels. We give the corresponding counterexamples.

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Veröffentlicht in:Russian mathematics 2019-09, Vol.63 (9), p.63-83
1. Verfasser: Shcherbakov, V. I.
Format: Artikel
Sprache:eng
Schlagworte:
Dirichlet problem
Fourier series
Mathematics
Mathematics and Statistics
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Zusammenfassung:In this paper, we prove that in symmetric Dini tests with respect to Price and generalized Haar systems both conditions are essential; no one of them alone guarantees the convergence of the Fourier series independently of the majorant of Dirichlet kernels. We give the corresponding counterexamples.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X1909007X