1,384 research outputs found
Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings
Let be a probability measure with an infinite compact support on
. Let us further assume that is a sequence of
orthogonal polynomials for where is a sequence of
nonlinear polynomials and for all
. We prove that if there is an such that
is a root of for each then the distance between any two
zeros of an orthogonal polynomial for of a given degree greater than
has a lower bound in terms of the distance between the set of critical points
and the set of zeros of some . Using this, we find sharp bounds from below
and above for the infimum of distances between the consecutive zeros of
orthogonal polynomials for singular continuous measures.Comment: Contains less typo
National project for the evaluation of ERTS imagery applications to various earth resources problems of Turkey
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Orthogonal polynomials on generalized Julia sets
We extend results by Barnsley et al. about orthogonal polynomials on Julia
sets to the case of generalized Julia sets. The equilibrium measure is
considered. In addition, we discuss optimal smoothness of Green functions and
Parreau-Widom criterion for a special family of real generalized Julia sets.Comment: We changed the second part of the article a little bit and gave
sharper results in this versio
Orthogonal polynomials for the weakly equilibrium Cantor sets
Let be the weakly equilibrium Cantor type set introduced in [10].
It is proven that the monic orthogonal polynomials with respect to
the equilibrium measure of coincide with the Chebyshev polynomials
of the set. Procedures are suggested to find of all degrees and the
corresponding Jacobi parameters. It is shown that the sequence of the Widom
factors is bounded below
Two Measures on Cantor Sets
We give an example of Cantor type set for which its equilibrium measure and
the corresponding Hausdorff measure are mutually absolutely continuous. Also we
show that these two measures are regular in Stahl-Totik sense
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