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Gérard-Sibuya's versus Majima's concept of asymptotic expansion in several variables

Part of: Asymptotic theory Approximations and expansions

Published online by Cambridge University Press:  09 April 2009

J. A. Hernández  and
J. Sanz
J. Sanz
Affiliation:
Depto. de Análisis Matemático Facultad de Ciencias Universidad de Valladolidc/ Prado de la Magdalena s/n 47005 ValladolidSpain e-mail: jaisla@am.uva.es e-mail: jsanzg@am.uva.es
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Abstract

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We give an example of a holomorphic function, admitting Gérard-Sibuya asymptotic expansion on a polysector of Cn, and such that none of its derivatives admits such an expansion. This motivates the study of the relationship between the concepts of asymptotic expansion in several variables respectively given by Gérard-Sibuya and Majima. For a function f, Majima's notion is proved to be equivalent, on the one hand, to the existence of Gérard-Sibuya asymptotic expansion for f and its derivatives, and on the other hand, to the boundedness of the derivatives of f on bounded proper subpolysectors of S.

MSC classification

Secondary: 34E05: Asymptotic expansions 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 21 - 35
Copyright
Copyright © Australian Mathematical Society 2001

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