- Tytuł:
- Entire functions of exponential type not vanishing in the half-plane \(\Im z > k\), where \(k > 0\)
- Autorzy:
- Hachani, Mohamed Amine
- Powiązania:
- https://bibliotekanauki.pl/articles/747061.pdf
- Data publikacji:
- 2017
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Inequalities
entire functions of exponential type
polynomial
trigonometric polynomial - Opis:
- 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.
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 1
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł