Asymptotic properties of zeros of orthogonal rational functions

[摘要] A sequence {x(m) : m = 0, 1, 2, ...} of real numbers gives rise to an absolutely continuous measure psi(N)((T)) on the unit circle given by [GRAPHICS] where N is a natural number, T is an element of (0, 1). Each measure psi(N)((T)) determines a sequence {Phi(n)((N,T))} of monic orthogonal rational functions with prescribed poles outside the closed unit disk. (In particular these rational functions may be polynomials.) A measure psi(0) with support consisting of the points xi 1, ..., xi(n0) on the unit circle is given. Let n > n(0). Under a suitable condition on weak* convergence of the measures and with a proper ordering of the zeros z(k)(n,N,T) of Phi(n)((N,T)), it can be shown that [GRAPHICS] and that there exists a positive number rho(n) < 1 such that \z(k)(n,N,T)\ less than or equal to rho(n) for k = n(0) + 1, ..., n, for all N and all T is an element of (0,1). The theory is applied to the problem of determining unknown frequencies in a trigonometric signal [GRAPHICS]

[发布日期] 1997-01-13

[效力级别]  Proceedings Paper

[关键词] zeros of orthogonal rational functions;frequency analysis