RT Journal Article
T1 Orthogonal polynomials and cubic polynomial mappings (I)
A1 Marcellán Español, Francisco José
A1 Petronilho, José
AB 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.
PB Mesa State College
YR 2000
FD 2000
LK https://hdl.handle.net/10016/6181
UL https://hdl.handle.net/10016/6181
LA eng
NO 29 pages, no figures.-- MSC1991 code: Primary 42C05.
NO MR#: MR1789676 (2001m:42047)
NO 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.
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RD 27 jul. 2024