On semiclassical orthogonal polynomials via polynomial mappings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Castillo, K.¹  de Jesus, M. N.²  Petronilho, J.¹ 

[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

[2] Polytechn Inst Viseu, ESTGV, CI&DETS IPV, Campus Politecn Repeses, P-3504510 Viseu, Portugal

关键词: Orthogonal polynomials;    Classical and semiclassical;    orthogonal polynomials;    Polynomial mappings;    Moment linear functionals;    Integral representations;   

DOI  :  10.1016/j.jmaa.2017.06.072

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free