ON REAL AND COMPLEX ZEROS OF ORTHOGONAL POLYNOMIALS IN A DISCRETE SOBOLEV SPACE

[摘要] Let {S(n)(x; c, N)} denote a set of polynomials orthogonal with respect to the discrete Sobolev inner product [f, g] = integral-infinity/-infinity f(x)g(x)dpsi(x) + Nf'(c)g'(c), where N greater-than-or-equal-to 0, c is-an-element-of R. For N = 0, put K(n)(x) = S(n)(x; ., 0). Then S(n)(x; c, N) has at least n - 2 different real zeros; their position with respect to the zeros of K(n) can be determined using the tangent to the graph of y = K(n)(x) in (c, K(n)(c)). On the other hand, if n greater-than-or-equal-to 3, then c can be chosen such that S(n)(x; c, N) has two complex zeros if N is sufficiently large.

[发布日期] 1993-12-31

[效力级别]  Proceedings Paper

[关键词] ORTHOGONAL POLYNOMIALS;SOBOLEV SPACES;ZEROS