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