Approximation of Bounded Holomorphic and Harmonic Functions by Fejér Means

Approximation of Bounded Holomorphic and Harmonic Functions by Fejér Means

We compute the exact values of the least upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a Voronovskaya-type formula in the case of approximation by Fejér means. We also present some consequences that are of independent interest.

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Veröffentlicht in:Ukrainian mathematical journal 2019-09, Vol.71 (4), p.589-618
Hauptverfasser: Savchuk, V. V., Chaichenko, S. O., Savchuk, M. V.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Approximation
Geometry
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Statistics
Upper bounds
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Beschreibung
Zusammenfassung:We compute the exact values of the least upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a Voronovskaya-type formula in the case of approximation by Fejér means. We also present some consequences that are of independent interest.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-019-01665-0