Cell structure of the space of real polynomials

Malyshev, V.

doi:10.1090/S1061-0022-04-00809-X

Cell structure of the space of real polynomials
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by V. A. Malyshev
Translated by: the author

St. Petersburg Math. J. 15 (2004), 191-248

DOI: https://doi.org/10.1090/S1061-0022-04-00809-X

Published electronically: January 27, 2004

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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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