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A direct theorem for strictly convex domains in ℂn

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Abstract

For a strictly covex C2-smooth domain Ω⊂ℂn and a function f ɛ Λα(Ω) holomorphic in Ω, we construct polynomials pN, deg pN<-N, such that

$$\left| {f(z) - p_N (z)} \right| \leqslant CN^{ - \alpha } ,z \in \bar \Omega .$$

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Authors
  1. N. A. Shirokov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 151–173.

Translated by A. A. Borichev.

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Shirokov, N.A. A direct theorem for strictly convex domains in ℂn . J Math Sci 80, 1972–1988 (1996). https://doi.org/10.1007/BF02367013

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  • DOI: https://doi.org/10.1007/BF02367013

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