A note on semi-classical orthogonal polynomials
Copyright policy )A note on semi-classical orthogonal polynomials
The author studies the characterization of semi-classical monic orthogonal polynomial sequences (MOPS). Orthogonality is defined with respect to a linear functional on the linear space of polynomials with real coefficients and the main results are twofold: (1) full characterization of classical MOPS (correction on \textit{F. Marcellán, A. Branquinho} and \textit{J. Petronilho} [Acta Appl. Math. 34, No. 3, 283-303 (1994; Zbl 0793.33009)]), (2) proof that the characterization property, in the form given in the previous item, can not be exteded to semi-classical MOPS. A nicely written note.
semi-classical linear functionals, monic orthogonal polynomial sequences, Orthogonal polynomials, 33C80, quasi-orthogonality, Spherical harmonics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 33C45
semi-classical linear functionals, monic orthogonal polynomial sequences, Orthogonal polynomials, 33C80, quasi-orthogonality, Spherical harmonics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 33C45
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