On Quantities of the Type of Modulus of Continuity and Analogs of $K$-Functionals in the Spaces $S^{(p,q)}(\sigma^{m-1})$

R. A. Lasuriya

Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 251-264.

Résumé

The paper continues the research of the author begun in 2003–2021. Quantities of the type of modulus of continuity of functions defined on the sphere in the space $S^{(p,q)}(\sigma^{m-1})$ are studied. These quantities are generated by a family of operators of multiplier type. Their equivalence to analogs of $K$-functionals is established.

Détail

Keywords: Fourier–Laplace series, $\psi$-derivative, best approximation, modulus of continuity, $K$-functional.

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