In this paper we consider the space Ap 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 Ap and Aq are mutually conjugate. In each of these spaces we introduce the orthonormal system
whereϕ is the conformal mapping of the region onto the unit disc. We prove it is dense and determine when it will be a basis.
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Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 411–420, September, 1975.
In conclusion I wish to thank S. G. Kreyn for a discussion of these results.
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Shikhvatov, A.M. Spaces of analytic functions in a region with an angle. Mathematical Notes of the Academy of Sciences of the USSR 18, 833–839 (1975). https://doi.org/10.1007/BF01095441
- Analytic Function
- Unit Disc
- Conformal Mapping
- Orthonormal System