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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| Vydáno v: | Russian mathematics Ročník 62; číslo 1; s. 65 - 69 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.01.2018
Springer Nature B.V |
| Témata: | |
| ISSN: | 1066-369X, 1934-810X |
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| Abstract | 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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| AbstractList | 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. |
| Author | Mukhamadiev, E. Naimov, A. N. |
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| Cites_doi | 10.1134/S0012266116010079 |
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| Keywords | method of differential equations class of entire functions estimate of order of growth of function |
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| References | Mukhamadiev, Naimov, Sattorov (CR2) 2016; 52 Mukhamadiev, Baizaev (CR1) 2011; 142 Mukhamadiev, Naimov (CR3) 2014; 29 Demidovich (CR5) 1967 Demidovich, Maron (CR4) 1966 E. Mukhamadiev (9036_CR1) 2011; 142 B. P. Demidovich (9036_CR4) 1966 E. Mukhamadiev (9036_CR3) 2014; 29 B.P. Demidovich (9036_CR5) 1967 E. Mukhamadiev (9036_CR2) 2016; 52 |
| References_xml | – year: 1966 ident: CR4 publication-title: Foundations of Computational Mathematics – volume: 29 start-page: 187 issue: 2 year: 2014 end-page: 189 ident: CR3 article-title: Estimate of Order of Growth of One Family of Functions by Method of Differential Equations publication-title: Proceedings of International Scientific Conference ‘Contemporary Problems ofMathematics and the Teaching’ (Khujand) Uchen. zap. – volume: 142 start-page: 20 issue: 1 year: 2011 end-page: 25 ident: CR1 article-title: Bounded Solutions of Hyperbolic EquationsWith Constant Coefficients publication-title: Izv. AN Respubliki Tajikistan – volume: 52 start-page: 84 issue: 1 year: 2016 end-page: 91 ident: CR2 article-title: Bounded Solutions of a Class of Hyperbolic Equations on the Plane publication-title: Differential Equations doi: 10.1134/S0012266116010079 – year: 1967 ident: CR5 publication-title: Lectures on Mathematical Stability Theory – volume: 29 start-page: 187 issue: 2 year: 2014 ident: 9036_CR3 publication-title: Proceedings of International Scientific Conference ‘Contemporary Problems ofMathematics and the Teaching’ (Khujand) Uchen. zap. – volume-title: Foundations of Computational Mathematics year: 1966 ident: 9036_CR4 – volume-title: Lectures on Mathematical Stability Theory year: 1967 ident: 9036_CR5 – volume: 52 start-page: 84 issue: 1 year: 2016 ident: 9036_CR2 publication-title: Differential Equations doi: 10.1134/S0012266116010079 – volume: 142 start-page: 20 issue: 1 year: 2011 ident: 9036_CR1 publication-title: Izv. AN Respubliki Tajikistan |
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| SubjectTerms | Entire functions Mathematical analysis Mathematics Mathematics and Statistics Ordinary differential equations Partial differential equations Power series |
| Title | Estimate of the Order of Growth of a Class of Entire Functions on the Real Axis |
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