ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 62, Issue 1, pp 83–97 | Cite as

Generalized growth and approximation of entire function solution of Helmholtz equation in Banach spaces

Article
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Abstract

In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in \(R^2\) in Smirnov spaces [\(\varepsilon _p (S)\) and \(\varepsilon ^{^\prime }_p(S), 1\le p\le \infty \)] where S is finitely simply connected domain in the complex plane with the boundary that belongs to the Al’per class (Izv AN SSSR Ser Matem 19(3):423–444, 1955). Some bounds on generalized order and generalized type of entire solution of Helmholtz equation have been obtained in terms of the coefficients and approximation errors using function theoretic methods. Our results extend and improve the results of Kumar (J Appl Anal 18:179–196, 2012).

Keywords

Generalized order and type Helmholtz equation Polynomial approximation Smirnov space 

Mathematics Subject Classification

30B10 41A10 
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Copyright information

© Università degli Studi di Ferrara 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesAl-Baha UniversityAl-BahaKingdom of Saudi Arabia

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