Lp Extremal Ployomials in the Presence of a Denumerable Set of Mass Points (0 < p < 1) 0
Abstract
We study, for all p > 0 the asymptotic behavior of Lp extremal
polynomials with respect to the measure α = β + γ; α denotes a positive
measure whose support is the unit circle Γ plus a denumerable set of mass
points, which accumulate at Γ and satisfy Blaschke’s condition and β = βa +
βs, the absolutely continuous part of the measure satisfies Szegö condition.
Our main result is the explicit strong asymptotic formulas for the Lp extremal
polynomials.
polynomials with respect to the measure α = β + γ; α denotes a positive
measure whose support is the unit circle Γ plus a denumerable set of mass
points, which accumulate at Γ and satisfy Blaschke’s condition and β = βa +
βs, the absolutely continuous part of the measure satisfies Szegö condition.
Our main result is the explicit strong asymptotic formulas for the Lp extremal
polynomials.
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