Bohrs power series theorem and local Banach space theory

Defant, Andreas; Garcı́a, Domingo; Maestre, Manuel

doi:10.1515/crll.2003.030

Cited by 42 publications

(47 citation statements)

References 13 publications

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“…New proofs were given in [Sidon 1927;Tomić 1962]. More recently, attention has been paid to multidimensional generalizations of Bohr's theorem [Boas and Khavinson 1997;Boas 2000;Defant et al 2003;Dineen and Timoney 1989;1991]. Such generalizations were obtained by studying the power series of a holomorphic function defined in…”

Section: Taishun Liu and Jianfei Wangmentioning

confidence: 99%

An absolute estimate of the homogeneous expansions of holomorphic mappings

Liu¹,

Wang²

2007

Pacific J. Math.

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Section: Taishun Liu and Jianfei Wangmentioning

confidence: 99%

An absolute estimate of the homogeneous expansions of holomorphic mappings

Liu¹,

Wang²

2007

Pacific J. Math.

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“…See also [16] and [2]. H. Bohr called attention to a formal connection between ordinary Dirichlet series and Taylor series in infinitely many variables ( [12] or [25]).…”

Section: Introductionmentioning

confidence: 99%

The Bohr inequality for ordinary Dirichlet series

2006

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Abstract. We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if f (s) = ∞ n=1 a n n −s with f ∞ := sup ℜs>0 |f (s)| < ∞, then ∞ n=1 |a n |n −2 ≤ f ∞ and even slightly better, and ∞ n=1 |a n |n −1/2 ≤ C f ∞ , C being an absolute constant.

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“…Other results about the Bohr radius for holomorphic functions can be found in [2], [5], [7]- [10]. We would like to call a special attention to the paper [16] in which the relation between the Bohr radius and the Banach-Mazur distance between Banach spaces was discovered.…”

mentioning

confidence: 97%