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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Vydané v:	Linear algebra and its applications Ročník 408; s. 151 - 160
Hlavný autor:	Walker, Ronald A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY Elsevier Inc 01.10.2005 Elsevier Science
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Walker, Ronald A.
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Keywords	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
Language	English
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SubjectTerms	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
Title	Linear dependence of quotients of analytic functions of several variables with the least subcollection of generalized Wronskians
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