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 Mat. Zametki, 1977, Volume 22, Issue 2, Pages 277–283 (Mi mz8048)

Completeness of analytic functions and extremality of the coefficients of a Laurent series

S. O. Sinanyan

Moscow Power Engineering Institute

Abstract: We generalize Vitushkin's theorem on the fact that the completeness of the set of functions analytic on a compactum in the complex plane depends upon the extremality of the first coefficient of the Laurent series of the classes of functions connected with this compactum. We show that completeness is characterized by the extremality of the Laurent series coefficient with any fixed number $n$, $n\ge1$. The $n$-th analytic capacity considered, generalizing the concept of analytic capacity ($n=1$), also flexibly measures the set.

Full text: PDF file (441 kB)

English version:
Mathematical Notes, 1977, 22:2, 646–649

Bibliographic databases:

UDC: 517.5

Citation: S. O. Sinanyan, “Completeness of analytic functions and extremality of the coefficients of a Laurent series”, Mat. Zametki, 22:2 (1977), 277–283; Math. Notes, 22:2 (1977), 646–649

Citation in format AMSBIB
\Bibitem{Sin77} \by S.~O.~Sinanyan \paper Completeness of analytic functions and extremality of the coefficients of a~Laurent series \jour Mat. Zametki \yr 1977 \vol 22 \issue 2 \pages 277--283 \mathnet{http://mi.mathnet.ru/mz8048} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=460650} \zmath{https://zbmath.org/?q=an:0358.30001} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 2 \pages 646--649 \crossref{https://doi.org/10.1007/BF01780975}