Orthogonal polynomials and cubic polynomial mappings (I)

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dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Petronilho, José
dc.date.accessioned 2009-12-21T10:10:24Z
dc.date.available 2009-12-21T10:10:24Z
dc.date.issued 2000
dc.identifier.bibliographicCitation Communications in the Analytic Theory of Continued Fractions, 2000, n. 8, p. 88-116
dc.identifier.uri http://hdl.handle.net/10016/6181
dc.description 29 pages, no figures.-- MSC1991 code: Primary 42C05.
dc.description MR#: MR1789676 (2001m:42047)
dc.description.abstract We present characterization theorems for orthogonal polynomials obtained from a given system of orthogonal polynomials by a cubic polynomial transformation in the variable. Since such polynomials are the denominators of the approximants for the expansion in continued fractions of the x-transform of the moment sequences associated with the linear functionals with respect to which such polynomials are orthogonal, we state the explicit relation for the corresponding formal Stieltjes series. As an application, we study the eigenvalues of a tridiagonal 3-Toeplitz matrix. Finally, we deduce the second-order linear differential equation satisfied by the new family of orthogonal polynomials when the initial family satisfies such a kind of differential equation.
dc.description.sponsorship The work of the first author was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01 and INTAS program, INTAS-93-0219 Ext. The work of the second author was supported by Junta Nacional de Investigação Científica e Tecnológica (JNICT) under grant BD976 and Centro de Matemática da Universidade de Coimbra (CMUC) of Portugal.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Mesa State College
dc.rights © Mesa State College
dc.subject.other Orthogonal polynomials
dc.subject.other Polynomial mappings
dc.subject.other Recurrence coefficients
dc.subject.other Stieltjes formal series
dc.subject.other Toeplitz matrices
dc.subject.other Sieved orthogonal polynomials
dc.title Orthogonal polynomials and cubic polynomial mappings (I)
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
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