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Orthogonality and recurrence for ordered Laurent polynomial sequences

✍ Scribed by C. Díaz-Mendoza; P. González-Vera; M. Jiménez Paiz; O. Njåstad

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
282 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

a b s t r a c t

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 , 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.

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