SOBOLEV ORTHOGONAL POLYNOMIALS WITH A SMALL NUMBER OF REAL ZEROS

[摘要] Let {S(n)lambda} denote a set of polynomials orthogonal with respect to the Sobolev inner product [f, g] = integral-3/-1 f(x) g(x) dx + lambda integral-1/-1) f'(x) g'(x) dx + integral-3/-1 f'(x) g'(x) dx,l where lambda greater-than-or-equal-to 0. If n is odd and lambda sufficiently large, then S(n)lambda has exactly one real zero. If n is even, n greater-than-or-equal-to 2, and lambda sufficiently large, then S' has exactly two real zeros. This result can be generalized to a more general inner product. (C) 1994 Academic Press, Inc.

[发布日期] 1994-06-01