Generalized harmonic Koebe functions
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- 作者：Á ; lvaro Ferrada-Salas<sup>asup><sup> ; sup><sup>1sup><sup> ; sup><sup>alferrada@mat.puc.cl" class="auth_mail" title="E-mail the corresponding authorsup> ; Marí ; a J. Martí ; n<sup>bsup><sup> ; sup><sup>2sup><sup> ; sup><sup>maria.martin@uef.fi" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：Harmonic mappings ; Affine and linear invariant families ; Koebe functions ; Taylor coefficients ; Extremal problems ; Growth and distortion
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2016
- 出版时间：1 March 2016
- 年：2016
- 卷：435
- 期：1
- 页码：860-873
- 全文大小：373 K
文摘
We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every Taylor coefficient as well as the growth and distortion of functions in affine and linear invariant families of complex-valued harmonic functions.