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Analytic Functions in the Unit Ball

Name: Analytic Functions in the Unit Ball
Brand: LAP Lambert Academic Publishing
SKU: 18095999
Price: 25.69 EUR
Availability: InStock
Author: Andriy Bandura
ISBN: 9786202017947

Bounded of L-index in Joint Variables and Solutions of Systems of PDE's

Andriy Bandura

Oleh Skaskiv

Language

English

Book Paperback

Libristo code: 18095999

Publishers LAP Lambert Academic Publishing, August 2017

A concept of boundedness of the L-index in joint variables is considered for function which are anal... Full description

Libristo code: 18095999

63 b

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A concept of boundedness of the L-index in joint variables is considered for function which are analytic in a ball. There are proved criteria of boundedness of the L-index in joint variables which describe local behavior of partial derivatives and maximum modulus on a skeleton of a polydisc, properties of power series expansion. Also we obtained analog of Hayman's Theorem. As a result, they are applied to study linear higher-order systems of partial differential equations and to deduce sufficient conditions of boundedness of the L-index in joint variables for their analytic solutions and to estimate its growth. Mainly, we used an exhaustion of the unit ball by polydiscs and by balls of lesser radii. Also growth estimates of analytic functions of bounded L-index in joint variables are obtained. Note that the concept of bounded L-index in joint variables have few advantages in the comparison with traditional approaches to study properties of analytic solutions of differential equations. In particular, if an analytic solution has bounded index then it immediately yields its growth estimates, an uniform distribution of its zeros, a certain regular behavior of the solution, etc.