On an extremal problem

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1958 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Academiae Scientiarum Hungaricae, volume 9, pages 309-313 (issn: 0001-5954, eissn: 1588-2632,

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Authors: Dancs, I.;

doi: 10.1007/bf02020259

On an extremal problem

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Abstract

Nach \textit{P. Turán} [Eine neue Methode in der Analysis und deren Anwendungen. Budapest: Akadémiai Kiadó (1953; Zbl 0052.04601)] ist \[ \min_{m+1\leq t\leq m+k} | a_1z_1^t+\cdots+a_kz_k^t| \bigg/\min_{1\leq j\leq k} | z_j|^t\geq\biggl|\sum_{j=1}^ka_j\biggr|\biggl(\frac {k}{2e(m+k)}\biggr)^{k-1}C, \] wo die \(a\) und \(z\) beliebige komplexe Zahlen und \(C=k/2e(m+k)\) ist. Verf. zeigt nun, daß der Satz mit \(C=1/2e\) richtig bleibt.

Keywords

Turán theory, Turán powersum theory, Power series (including lacunary series) in one complex variable

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