A Favard theorem for orthogonal rational functions on the unit circle |
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| Authors: | Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad |
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| Institution: | (1) Department of Computer Science, K.U. Leuven, B-3001, Leuven, Belgium;(2) Facultad de Matemáticas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands, Spain;(3) Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;(4) Department of Mathematics, University of Trondheim-NTH, N-7034 Trondheim, Norway |
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| Abstract: | We consider forn=0, 1,... the nested spaces 
n
of rational functions of degreen at most with given poles
. Given a finite measure supported on the unit circle, we associate with it a nested orthogonal basis of rational functions  0,...,
n
for
n
,n=0, 1,.... These
n
satisfy a recurrence relation that generalizes the recurrence for Szeg polynomials.In this paper we shall prove a Favard type theorem which says that if one has a sequence of rational functions
n
n
which are generated by such a recurrence, then there will be a measure  supported on the unit circle to which they are orthogonal. We shall give a sufficient condition for the uniqueness of this measure. |
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| Keywords: | |
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