Result: ON THE GROWTH OF ENTIRE FUNCTIONS REPRESENTED BY REGULARLY CONVERGENT FUNCTION SERIES: On the growth of entire functions represented by regularly convergent function series
Title:
ON THE GROWTH OF ENTIRE FUNCTIONS REPRESENTED BY REGULARLY CONVERGENT FUNCTION SERIES: On the growth of entire functions represented by regularly convergent function series
Authors:
Source:
Mathematics of the USSR-Sbornik. 29:281-302
Publisher Information:
Steklov Mathematical Institute, 1976.
Publication Year:
1976
Subject Terms:
Representations of entire functions of one complex variable by series and integrals, 0103 physical sciences, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal
Article
File Description:
application/xml
ISSN:
0025-5734
DOI:
10.1070/sm1976v029n02abeh003668
Access URL:
Accession Number:
edsair.doi.dedup.....c0b6d5d3b950cf3a12f2bc99621e3a93
Database:
OpenAIRE
Further Information
The first part of the article is devoted to the investigation of the growth of entire functions represented by the polynomial series of Abel-Goncarov and Newton, and by Taylor series with variable centering. Under certain assumptions about the sequence of interpolation nodes, we find both the order and sharp lower and upper estimates for the type of an entire function represented by an Abel-Goncarov series. Making various assumptions about the interpolation nodes, we find both the order and a sharp upper estimate for the indicator of an entire function represented by Newton's series, as well as sharp lower and upper estimates for the type of such a function.Bibliography: 14 titles.