Abstract. The Bloch-Landau Theorem is one of the basic results in the geometric theory of holomorphic functions. It establishes that the image of the open unit disc D under a holomorphic function f (such that f (0) = 0 and f ′ (0) = 1) always contains an open disc with radius larger than a universal constant. In this paper we prove a Bloch-Landau type Theorem for slice regular functions over the skew field H of quaternions. This result is not at all a direct extension of the complex one, but heavily resents of the peculiarities of the quaternionic setting.

A Bloch-Landau Theorem for slice regular functions / Della Rocchetta, Chiara; Gentili, Graziano; Sarfatti, Giulia. - STAMPA. - (2013), pp. 55-74. [10.1007/978-88-470-2445-8_4]

A Bloch-Landau Theorem for slice regular functions

SARFATTI, GIULIA
2013-01-01

Abstract

Abstract. The Bloch-Landau Theorem is one of the basic results in the geometric theory of holomorphic functions. It establishes that the image of the open unit disc D under a holomorphic function f (such that f (0) = 0 and f ′ (0) = 1) always contains an open disc with radius larger than a universal constant. In this paper we prove a Bloch-Landau type Theorem for slice regular functions over the skew field H of quaternions. This result is not at all a direct extension of the complex one, but heavily resents of the peculiarities of the quaternionic setting.
2013
Advances in Hypercomplex Analysis
9788847024441
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/272333
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