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St. Petersburg Mathematical Journal

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Cell structure of the space of real polynomials


Author: V. A. Malyshev
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 2.
Journal: St. Petersburg Math. J. 15 (2004), 191-248
MSC (2000): Primary 26C10, 57Q15, 41A50
DOI: https://doi.org/10.1090/S1061-0022-04-00809-X
Published electronically: January 27, 2004
MathSciNet review: 2052131
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Abstract | References | Similar Articles | Additional Information

Abstract: The space of real polynomials is endowed with cell decompositions such that all polynomials in a single cell have the same root structure on the unit interval, the half-line, or the real line. These decompositions are used to investigate relationship between the roots and extrema of a polynomial, to construct an interpolation polynomial with free knots that increases or decreases simultaneously with the data, and to classify the Abel equations arising in the problem of Chebyshev approximation with fixed coefficients.


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Additional Information

V. A. Malyshev
Affiliation: Rybinsk State Avia-Technological Academy, Russia
Email: wmal@ryb.adm.yar.ru

DOI: https://doi.org/10.1090/S1061-0022-04-00809-X
Keywords: Positive polynomials, cell decompositions
Received by editor(s): January 18, 2002
Published electronically: January 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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