AVERAGING SETS ON THE UNIT-CIRCLE

[摘要] For every normalized measure sigma on the unit circle T let t(sigma)(n) be the maximal integer t such that the quadrature formula of Chebyshev type [GRAPHICS] holds for some subset {(x(1), y(1)),...(x(n), y(n))) of T and for all polynomials p(x, y) of deg p less than or equal to t. If omega is the Lebesgue measure then t(omega)(n)= n - 1. Moreover, t(sigma)(n)less than or equal to n-1 for every sigma. Under the Kolmogorov-Szego condition on sigma we prove that sigma = omega if t(sigma)(n) = n - 1 for a subsequence of n = 1, 2, 3,.... (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01