Classes of $(\psi, \beta)$-differential functions of complex variable and approximation by linear averages of their Faber series
We introduce the notion of $(\psi, \beta)$-derivative of a function of one complex variable, and define on the basis of this the classes $L_\beta ^{\psi}{\mathfrak N} (G)$  of $(\psi, \beta)$-differentiable analytic functions in a bounded domain $G$. The classes $L_\beta ^{\psi}{\mathfr...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8259 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We introduce the notion of $(\psi, \beta)$-derivative of a function of one complex variable, and define on the basis of this the classes $L_\beta ^{\psi}{\mathfrak N} (G)$  of $(\psi, \beta)$-differentiable analytic functions in a bounded domain $G$. The classes $L_\beta ^{\psi}{\mathfrak N} (G)$ consist of the Cauchy-type integrals whose densities $f(\zeta)$ are such that the induced functions $\tilde f(t)$  on the unit circle are periodic functions of classes $L_\beta ^{\psi}{\mathfrak N}$. We consider approximation of functions $f\in L_\beta ^{\psi}{\mathfrak N} (G)$  by algebraic polynomials constructed from their series expansions in Faber polynomials. |
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