Deformation of Minimal Polynomials and Approximation of Several Intervals by an Inverse Polynomial Mapping |
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Authors: | Franz Peherstorfer |
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Institution: | Johannes Kepler Universität Linz, Institut für Analysis und Numerik, Linz-Auhof, A-4040, Austria |
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Abstract: | In this paper we show that for a given set of l real disjoint intervals El=lj=1 a2j−1, a2j] and given >0 there exists a real polynomial
and a set of l disjoint intervals El=lj=1 ã2j−1, ã2j] with ElEl and (ã1, …, ã2l)−(a1, …, a2l)max<, such that
−1(−1, 1])=El. The statement follows by showing how to get in a constructive way by a continuous deformation procedure from a minimal polynomial on El with respect to the maximum norm a polynomial mapping of El. |
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