Farrell–Markushevich Theorem

(Theory)

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What is Farrell–Markushevich theorem?

In mathematics, the Farrell–Markushevich theorem, proved independently by O. J. Farrell (1899–1981) and A. I. Markushevich (1908–1979) in 1934, is a result concerning the approximation in mean square of holomorphic functions on a bounded open set in the complex plane by complex polynomials. It states that complex polynomials form a dense subspace of the Bergman space of a domain bounded by a simple closed Jordan curve. The Gram–Schmidt process can be used to construct an orthonormal basis in the Bergman space and hence an explicit form of the Bergman kernel, which in turn yields an explicit Riemann mapping function for the domain.

Technology Types

mathematical theoremoperator theorypropositionstatementtheoremtheorems in complex analysistheorems in functional analysistheory

Synonyms

Farrell-Markushevich theorem

Translations

Farrell–Markusjevitjs sats (sv)

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