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Widom factors for the Hilbert norm

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Alpan G., Goncharov A.

Banach Center Publications

2015

tom 107

nr 1

11-18

Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence $(W²ₙ(μ))_{n=0}^{∞}$ has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze the behavior of the corresponding limit as a function of the parameters and review some other examples of measures when Widom factors can be evaluated.

Ograniczanie wyników

1 Banach Center Publications

1 Alpan G.

1 Goncharov A.

1 2015

Wyniki wyszukiwania

Widom factors for the Hilbert norm