On linear operators preserving the set of positive polynomials

Alexander Guterman; Boris Shapiro

On linear operators preserving the set of positive polynomials

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Following the classical approach of Pólya-Schur theory [13] 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.

Original language	English
Pages (from-to)	411-429
Number of pages	19
Journal	Journal of Fixed Point Theory and Applications
Volume	3
Issue number	2
State	Published - Sep 2008
Externally published	Yes

Bibliographical note

Funding Information:
The authors are grateful to Petter Bränden for important references, to Julius Borcea for discussions, and to Claus Scheiderer for the interest in our work. The first author is sincerely grateful to the Wenner-Gren Foundation, the Swedish Royal Academy of Sciences and the Mittag-Leﬄer Institute for supporting his visit to Stockholm in Spring 2007 when a substantial part of this project was

Keywords

Linear preservers
Non-negative and elliptic polynomials
Positive
Pólya-Schur theory

Cite this

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abstract = "Following the classical approach of P{\'o}lya-Schur theory [13] 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.",

keywords = "Linear preservers, Non-negative and elliptic polynomials, Positive, P{\'o}lya-Schur theory",

author = "Alexander Guterman and Boris Shapiro",

note = "Funding Information: The authors are grateful to Petter Br{\"a}nden for important references, to Julius Borcea for discussions, and to Claus Scheiderer for the interest in our work. The first author is sincerely grateful to the Wenner-Gren Foundation, the Swedish Royal Academy of Sciences and the Mittag-Leﬄer Institute for supporting his visit to Stockholm in Spring 2007 when a substantial part of this project was",

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AU - Shapiro, Boris

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N2 - Following the classical approach of Pólya-Schur theory [13] 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.

AB - Following the classical approach of Pólya-Schur theory [13] 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.

KW - Linear preservers

KW - Non-negative and elliptic polynomials

KW - Positive

KW - Pólya-Schur theory

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ER -

On linear operators preserving the set of positive polynomials

Abstract

Bibliographical note

Keywords

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Cite this