On linear operators preserving the set of positive polynomials
نویسندگان
چکیده
منابع مشابه
On Linear Operators Preserving the Set of Positive Polynomials
Following the classical approach of Pólya-Schur theory [14] we initiate in this paper the study of linear operators acting on R[x] and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.
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We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of FischerFock dualities, Hankel forms, and convolutions with non-negative measures. We also establish higher-dimensional analogs of these results. In particular, our classificati...
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ژورنال
عنوان ژورنال: Journal of Fixed Point Theory and Applications
سال: 2008
ISSN: 1661-7738,1661-7746
DOI: 10.1007/s11784-008-0084-3