| Resumo: |
On the real line there is an important theorem, known as Favard’s Theorem, which guaran- tees the existence of a single probability measure in relation to which certain polynomials, which satisfy a three-term recurrence relation, are orthogonal. For the unit circle there is a known version of this result, however the measure obtained is such that the respec- tive orthogonal polynomials do not satisfy a recurrence relation of three terms as in the real case. The objective of this work is to study a theorem of Favard type for the unit circle associated with polynomials that satisfy a three-term recurrence relation in which the coefficients that appear in the recurrence formula are real sequences, one of which is a positive chained sequence. The methodology applied in this work was bibliographical research, which used, for the theoretical foundation, materials found in databases such as Scielo, CAPES, University websites, as well as printed materials, scientific articles, dis- sertations, theses, magazines and other periodicals. The literature review proposed here shows the importance of studying and connecting the Theory of continued fractions and positive chained sequences to characterize non-trivial probability measures in the unit circle. |
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