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Integral means spectrum and the modified Bessel function of zero order


Author: I. R. Kayumov
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 17 (2005), nomer 3.
Journal: St. Petersburg Math. J. 17 (2006), 453-463
MSC (2000): Primary 30C35
DOI: https://doi.org/10.1090/S1061-0022-06-00914-9
Published electronically: March 9, 2006
MathSciNet review: 2167846
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Abstract | References | Similar Articles | Additional Information

Abstract: A new characteristic $ \beta^*_f(t)$ of a conformal mapping $ f$ of the disk $ \Bbb D$ onto a simply connected domain is introduced and its relationship with the so-called integral means spectrum $ \beta_f(t)$ is studied. The Brennan conjecture (saying that $ \beta_f(-2)\le 1$) is confirmed in the case where the Taylor series of $ \log f'(z)$ is Hadamard lacunary with sufficiently large lacunarity exponent.


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Additional Information

I. R. Kayumov
Affiliation: Kazan State University, Kazan, Russia
Email: ikayumov@ksu.ru

DOI: https://doi.org/10.1090/S1061-0022-06-00914-9
Keywords: Conformal mapping, $\ast$-spectrum of integral means, modified Bessel function
Received by editor(s): June 15, 2004
Published electronically: March 9, 2006
Additional Notes: This article was supported in part by RFBR (grants no. 05–01–00523 and 03-01-00015), and by the NIOKR AN RT foundation
Article copyright: © Copyright 2006 American Mathematical Society

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