Linear dependence of quotients of analytic functions of several variables with the least subcollection of generalized Wronskians

We study linear dependence in the case of quotients of analytic functions in several variables (real or complex). We identify the least subcollection of generalized Wronskians whose identical vanishing is sufficient for linear dependence. Our proof admits a straight-forward algebraic generalization...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 408; pp. 151 - 160
Main Author: Walker, Ronald A.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.10.2005
Elsevier Science
Subjects:
Algebra
Analytic functions of several variables
Exact sciences and technology
Generalized Wronskians
Higher-dimensional partitions
Linear and multilinear algebra, matrix theory
Linear dependence
Mathematics
Sciences and techniques of general use
Young-like sets
Higher-dimensional partitions
Linear dependence
32A20
15A54
Young-like sets
Generalized Wronskians
15A03
Analytic functions of several variables
32A20 Linear dependence
Young- like sets
Linear relation
Multivariate analysis
Generalized
Wronskian
Quotient
Analytical function
ISSN:0024-3795, 1873-1856
Online Access:Get full text
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Summary:We study linear dependence in the case of quotients of analytic functions in several variables (real or complex). We identify the least subcollection of generalized Wronskians whose identical vanishing is sufficient for linear dependence. Our proof admits a straight-forward algebraic generalization and also constitutes an alternative proof of the previously known result that the identical vanishing of the whole collection of generalized Wronskians implies linear dependence. Motivated by the structure of this proof, we introduce a method for calculating the space of linear relations. We conclude with some reflections about this method that may be promising from a computational point of view.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2005.06.002