A Favard theorem for orthogonal rational functions on the unit circle | Zendy

Adhemar Bultheel | Zendy; Pablo González-Vera | Zendy; Erik Hendriksen | Zendy; Olav Njåstad | Zendy

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A Favard theorem for orthogonal rational functions on the unit circle

Author(s) -

Adhemar Bultheel,

Pablo González-Vera,

Erik Hendriksen,

Olav Njåstad

Publication year - 1992

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/bf02141918

Subject(s) - mathematics , unit circle , recurrence relation , measure (data warehouse) , rational function , unit (ring theory) , combinatorics , sequence (biology) , orthogonal polynomials , uniqueness , pure mathematics , discrete mathematics , mathematical analysis , mathematics education , database , biology , computer science , genetics

We consider for n=0,1,... the nested spaces L_n of rational functions of degree n at most with given poles 1/ã_i, |ã_i|<1, i=1,...,n. It is known that, given a measure supported on the unit circle, it is possible to generate a nested orthogonal basis fn in Ln of rationals. These satisfy a recurrence relation that generalizes the recurrence for Szegö polynomials.In this paper we shall prove a Favard type theorem which says that if you have a sequence of rational functions fn in L_n which are generated by such a recurrence,then there will be a measure µ supported on the unit circle to which they are orthogonal. We shall give a sufficient condition for the uniqueness of this measure.status: publishe

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