2 00 2 Measures and semi - orthogonal functions on the unit circle
نویسندگان
چکیده
The zeros of semi-orthogonal functions with respect to a probability measure µ supported on the unit circle can be applied to obtain Szeg˝ o quadrature formulas. The discrete measures generated by these formulas weakly converge to the orthogonality measure µ. In this paper we construct families of semi-orthogonal functions with interlacing zeros, and give a representation of the support of µ in terms of the asymptotic distribution of such zeros. distribution of zeros, Support of a measure. Given a probability measure ν on the real line, it is well known (see for example [5] or [4]) that a sequence of orthogonal polynomials (SOP), p n n∈N , with respect to ν, satisfies the following properties: a) The zeros of p n are real and simple for n ≥ 1.
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