Orthogonality and recurrence for ordered Laurent polynomial sequences

[摘要] We consider orderings of nested subspaces of the space of Laurent polynomials on the real line, more general than the balanced orderings associated with the ordered bases {1, z(-1), z, z(-2). z(2),...} and {1, z, z(-1), z(-2),...). We show that with such orderings the sequence of orthonormal Laurent polynomials determined by a positive linear functional satisfies a three-term recurrence relation. Reciprocally, we show that with such orderings a sequence of Laurent polynomials which satisfies a recurrence relation of this form is orthonormal with respect to a certain positive functional. (C) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-15

[效力级别]  Proceedings Paper

[关键词] Orthonormal Laurent polynomials;Three-term recurrence relation;Favard-type theorem