Linear Differential Elimination for Analytic Functions

This paper provides methods to decide whether a given analytic function of several complex variables is a linear combination of finitely many given analytic functions with coefficients of the following special form: Each one of these coefficients is a composition of an unknown analytic function of l...

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Bibliographic Details
Published inMathematics in computer science Vol. 4; no. 2-3; pp. 231 - 242
Main Authors Plesken, Wilhelm, Robertz, Daniel
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.09.2010
Subjects
Computer Science
Mathematics
Mathematics and Statistics
Differential elimination
Primary 12H05
Functional dependence
Secondary 13N10
Linear pde’s
Analytic function
Janet basis
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Summary:This paper provides methods to decide whether a given analytic function of several complex variables is a linear combination of finitely many given analytic functions with coefficients of the following special form: Each one of these coefficients is a composition of an unknown analytic function of less arguments than the function to be expressed, with fixed analytic functions. Methods which compute suitable coefficient functions in the affirmative case are presented as well.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-010-0053-2