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Original Articles

On the existence of lacunary power series analytically continuable and bounded outside sectors

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Pages 669-676 | Received 24 Oct 2008, Accepted 22 Apr 2009, Published online: 02 Jul 2009

References

  • Polya , G . 1942 . On converse gap theorems . Trans. Am. Math. Soc. , 52 : 65 – 71 .
  • Bieberbach , L . 1955 . Analytische Fortsetzung , Berlin : Springer .
  • Koosis , P . 1992 . The Logarithmic Integral , Vol. II , Cambridge : Cambridge University Press .
  • Fuchs , WHJ . 1946 . A generalization of Carleson's theorem . J. London Math. Soc. , 21 : 106 – 110 .
  • Boas , RP . 1954 . Entire Functions , New York : Academic Press .
  • Anderson , JM . 1972 . Müntz–Szasz type approximation and the angular growth of lacunary integral functions . Trans. Am. Math. Soc. , 169 : 237 – 248 .
  • Martirosian , VA . 1986 . Entire functions that are bounded on a closed angle and representable by power series with lacunae or with real coefficients . Dokl. Akad. Nauk SSSR , 289 ( 6 ) : 1301 – 1304 . (Russian) (English translation: Soviet Math. Dokl. 34(1) (1987), pp. 224–226)
  • Hille , E . 1977 . Analytic Function Theory , Vol. II , New York : Chelsea .
  • Arakelian , NU . 1984 . On efficient analytic continuation of power series . Matem. Sbornik , 124 ( 166 ) : 24 – 44 . (Russian) (English translation: Math. USSR Sbornik 52(1) (1985), pp. 21–39)

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