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

Generalized growth and approximation of entire function solution of Helmholtz equation in Banach... In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in $$R^2$$ R 2 in Smirnov spaces [ $$\varepsilon _p (S)$$ ε p ( S ) and $$\varepsilon ^{^\prime }_p(S), 1\le p\le \infty $$ ε p ′ ( S ) , 1 ≤ p ≤ ∞ ] 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

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

Kumar, Devendra
ANNALI DELL'UNIVERSITA' DI FERRARA , Volume 62 (1) – Oct 16, 2015
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15 pages

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-015-0233-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in $$R^2$$ R 2 in Smirnov spaces [ $$\varepsilon _p (S)$$ ε p ( S ) and $$\varepsilon ^{^\prime }_p(S), 1\le p\le \infty $$ ε p ′ ( S ) , 1 ≤ p ≤ ∞ ] 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).

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Oct 16, 2015

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