Estimate of the Order of Growth of a Class of Entire Functions on the Real Axis

For a class of entire functions we study the problem of estimation of the order of growth of functions on the real axis. This problem is important for the justification of the integral representation of bounded solutions to certain partial differential equations considered in other papers of the aut...

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Bibliographic Details
Published in:Russian mathematics Vol. 62; no. 1; pp. 65 - 69
Main Authors: Mukhamadiev, E., Naimov, A. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.01.2018
Springer Nature B.V
Subjects:
Entire functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary differential equations
Partial differential equations
Power series
method of differential equations
class of entire functions
estimate of order of growth of function
ISSN:1066-369X, 1934-810X
Online Access:Get full text
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Summary:For a class of entire functions we study the problem of estimation of the order of growth of functions on the real axis. This problem is important for the justification of the integral representation of bounded solutions to certain partial differential equations considered in other papers of the authors. In order to obtain an estimate of the order of growth of a function on the real axis, we use the method of differential equations. The method is based, on one hand, on the construction of a system of first-order ordinary differential equations whose solution is a vector function of traces of function and its derivatives on the real axis. On the other hand, under the respective change of variables in the system of equations, we obtain an estimate of the solution to the system of equations for a large positive values of the argument. The obtained estimate is non-trivial and shows the way a complex parameter of a power series affects the order of growth of a function.
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ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X18010097