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This article is cited in 3 scientific papers (total in 3 papers)
Spaces of analytic functions in a region with an angle
A. M. Shikhvatov
Abstract:
In this paper we consider the space $A_p$ of analytic functions which are $p$-power integrable in a region with an angle. We find a set of numbers $p$ and $q$ ($1/p+1/q=1$) (which depend on the magnitude of the angle) for which the spaces $A_p$ and $A_q$ are mutually conjugate. In each of these spaces we introduce the orthonormal system
$$
e_n=\sqrt{(n+1)/\pi}\varphi'\varphi^n,\quad n=0,1,\dots
$$
where $\varphi$ is the conformal mapping of the region onto the unit disc. We prove it is dense and determine when it will be a basis.
Received: 28.02.1974
Citation:
A. M. Shikhvatov, “Spaces of analytic functions in a region with an angle”, Mat. Zametki, 18:3 (1975), 411–420; Math. Notes, 18:3 (1975), 833–839
Linking options:
https://www.mathnet.ru/eng/mzm7669 https://www.mathnet.ru/eng/mzm/v18/i3/p411
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Abstract page: | 154 | Full-text PDF : | 70 | First page: | 1 |
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