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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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
Published electronically: January 27, 2004
MathSciNet review: 2052131
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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

Keywords: Positive polynomials, cell decompositions
Received by editor(s): January 18, 2002
Published electronically: January 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society