On Zero-Preserving Linear Transformations

For an arbitrary subset I of R and for a function f defined on I, the number of zeros of f on I will be denoted byZI(f).In this paper we attempt to characterize all linear transformations T taking a linear subspace W of C(I) into functions defined on J (I,J⊆R) such thatZI(f)=ZJ(Tf)for all f∈W.

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 266; no. 1; pp. 237 - 258
Main Authors:	Carnicer, J.M., Peña, J.M., Pinkus, A.
Format:	Journal Article
Language:	English
Published:	San Diego, CA Elsevier Inc 01-02-2002 Elsevier
Subjects:	Exact sciences and technology Mathematics Sciences and techniques of general use
Online Access:	Get full text
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Summary:	For an arbitrary subset I of R and for a function f defined on I, the number of zeros of f on I will be denoted byZI(f).In this paper we attempt to characterize all linear transformations T taking a linear subspace W of C(I) into functions defined on J (I,J⊆R) such thatZI(f)=ZJ(Tf)for all f∈W.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.2001.7745