On some approximate properties of biharmonic Poisson integrals in the integral metric (Q6589508)
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scientific article; zbMATH DE number 7898635
| Language | Label | Description | Also known as |
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| English | On some approximate properties of biharmonic Poisson integrals in the integral metric |
scientific article; zbMATH DE number 7898635 |
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On some approximate properties of biharmonic Poisson integrals in the integral metric (English)
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19 August 2024
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In the paper, the authors obtain asymptotic equalities for the upper bounds of deviations of \((\psi, \beta)\)-differentiable functions from their biharmonic Poisson integrals in the integral metric. This solves the corresponding Kolmogorov-Nikol'skii problem on the classes \(L^{\psi}_{\beta,1}\) of functions with generalized derivative, introduced by \textit{A. I. Stepanets} [Методы теории приближений. I (Russian). Kyïv: Instytut Matematyky NAN Ukraïny (2002; Zbl 1129.42001)].
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generalized derivative
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Kolmogorov-Nikol'skii problem
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biharmonic Poisson integral
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