Treffer: A generalization of the Lindelöf theorem: Generalization of the Lindelöf theorem

Title:
A generalization of the Lindelöf theorem: Generalization of the Lindelöf theorem
Authors:
M. V. Zabolotskii, M. N. Sheremeta
Source:
Ukrainian Mathematical Journal. 50:1346-1364
Publisher Information:
Springer Science and Business Media LLC, 1998.
Publication Year:
1998
Subject Terms:
Representations of entire functions of one complex variable by series and integrals, Lindelöf theorem, Taylor series, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences, entire transcendental function
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1573-9376
0041-5995
DOI:
10.1007/bf02525242
Access URL:
https://link.springer.com/article/10.1007/BF02525242
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....f3bbd9d6a5ce6b096fc132c607b6467a
Database:
OpenAIRE

Weitere Informationen

Summary: It is proposed a generalization of the Lindelöf theorem on conditions on coefficients of the Taylor series of the entire transcendental function \(f\) in order that the relation \(\ln M_{f}(r)\sim\tau r^{\rho}\), \(r\to\infty\), \(M_{f}(r) = \max\{|f(r)|:|z|= r\}\) holds true.