Extremal polynomials on a Jordan arc

• Let gamma be a C2+ Jordan arc and let gamma(0) be the open arc which consists of interior points of gamma. We find concrete upper and lower bounds for the limit of Widom factors for L-2(mu) extremal polynomials on gamma & nbsp;which was given in Widom (1969). In addition, we show that the upper bound for the limit supremum of Widom factors for the weighted Chebyshev polynomials which was obtained in Widom (1969) can be improved once two normal derivatives of the Green function do not agree at one point z is an element of gamma(0). We also show that if gamma(0) is not analytic then we have improved upper bounds.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Widom factors

Chebyshev polynomials

Orthogonal polynomials

Extremal polynomials

Jordan arc

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