Title
Orthogonality and recurrence for ordered Laurent polynomial sequences
Abstract
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.
Year
DOI
Venue
2010
10.1016/j.cam.2010.07.013
J. Computational Applied Mathematics
Keywords
Field
DocType
orthonormal laurent,positive linear functional satisfies,laurent polynomial sequence,three-term recurrence relation,real line,nested subspaces,balanced ordering,recurrence relation,laurent polynomial,satisfiability
Positive linear functional,Polynomial,Mathematical analysis,Recurrence relation,Real line,Linear subspace,Laurent series,Orthonormal basis,Laurent polynomial,Mathematics
Journal
Volume
Issue
ISSN
235
4
0377-0427
Citations 
PageRank 
References 
4
0.53
1
Authors
4
Name
Order
Citations
PageRank
C. Díaz-Mendoza1204.56
P. González-Vera2469.45
M. Jiménez Paiz3183.14
O. Njåstad4101.96