On semiclassical orthogonal polynomials via polynomial mappings
| Autor: | M. N. de Jesus, J. Petronilho, K. Castillo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
polynomial mappings
Discrete mathematics Pure mathematics Applied Mathematics Discrete orthogonal polynomials 010102 general mathematics Biorthogonal polynomial 010103 numerical & computational mathematics classical and semiclassical orthogonal polynomials 01 natural sciences Classical orthogonal polynomials symbols.namesake moment linear functionals Wilson polynomials Hahn polynomials Orthogonal polynomials symbols Jacobi polynomials 0101 mathematics orthogonal polynomials Analysis Koornwinder polynomials Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.06.072 |
| Popis: | We consider orthogonal polynomials via polynomial mappings in the framework of the semiclassical class. We prove that this class is stable under polynomial transformations. Several consequences of this fact are deduced. As an application we analyze in detail cubic transformations for semiclassical orthogonal polynomials of class at most 2, recovering and extending some results proved recently for class 1, and producing new examples of semiclassical orthogonal polynomials of class 2. In particular, we show how to obtain integral representations for the regular functionals with respect to which these new semiclassical families are orthogonal. |
| Databáze: | OpenAIRE |
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