Integral means spectrum and the modified Bessel function of zero order
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I. R. Kayumov
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 17 (2006), 453-463
- DOI: https://doi.org/10.1090/S1061-0022-06-00914-9
- Published electronically: March 9, 2006
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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.References
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Bibliographic Information
- I. R. Kayumov
- Affiliation: Kazan State University, Kazan, Russia
- Email: ikayumov@ksu.ru
- 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
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 453-463
- MSC (2000): Primary 30C35
- DOI: https://doi.org/10.1090/S1061-0022-06-00914-9
- MathSciNet review: 2167846