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), 191248
MSC (2000):
Primary 26C10, 57Q15, 41A50
Published electronically:
January 27, 2004
MathSciNet review:
2052131
Fulltext PDF Free Access
Abstract 
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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 halfline, 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 AviaTechnological Academy, Russia
Email:
wmal@ryb.adm.yar.ru
DOI:
http://dx.doi.org/10.1090/S106100220400809X
PII:
S 10610022(04)00809X
Keywords:
Positive polynomials,
cell decompositions
Received by editor(s):
January 18, 2002
Published electronically:
January 27, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
