Entire functions of exponential type not vanishing in the half-plane \(\Im z > k\), where \(k > 0\)

• Autorzy: Mohamed Amine Hachani
• Języki publikacji: EN

Abstrakty

EN

Let \(P (z)\) be a polynomial of degree \(n\) having no zeros in \(|z| < k\), \(k \leq 1\), and let \(Q (z) := z^n \overline{P (1/{\overline {z}})}\). It was shown by Govil that if \(\max_{|z| = 1} |P^\prime (z)|\) and \(\max_{|z| = 1} |Q^\prime (z)|\) are attained at the same point of the unit circle \(|z| = 1\), then \[\max_{|z| = 1} |P'(z)| \leq \frac{n}{1 + k^n} \max_{|z| = 1} |P(z)|.\]The main result of the present article is a generalization of Govil's polynomial inequality to a class of entire functions of exponential type.

Słowa kluczowe

EN

Inequalities; entire functions of exponential type; polynomial; trigonometric polynomial

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2017
• Tom: 71
• Numer: 1

Daty

wydano

2017

online

2017-06-30

Twórcy

autor

Mohamed Amine Hachani

Bibliografia

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Identyfikatory

DOI

10.17951/a.2017.71.1.31