Orthonormal bases of polynomials in one complex variable

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dc.creatorCastrigiano, D. P. L.
dc.creatorKlopfer, W.
dc.date2000-11-28
dc.date.accessioned2026-07-07T04:38:53Z
dc.date.available2026-07-07T04:38:53Z
dc.descriptionLet a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_μ$ for some measure $μ$ on $\C$, if and o ly if the recurrence is a $3-$term relation with special coefficients. The supp rt of $μ$ lies on a straight line. This result is achieved by the analysis of a formally normal irreducible Hessenberg operator with only finitely many nonzero entries in every row. It generalizes the classical Favard's Theorem and the Representation Theorem.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0011240
dc.identifierhttp://arxiv.org/abs/math/0011240
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60457
dc.subjectFunctional Analysis
dc.subject41A10, 47B15
dc.titleOrthonormal bases of polynomials in one complex variable
dc.typetext

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