On the modifications of semi-classical orthogonal polynomials on nonuniform lattices

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• 作者：S. Mboutngam^a ; ^{mbsalif@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; M. Foupouagnigni^b ; ^{foupouagnigni@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; P. Njionou Sadjang^c ; ^{pnjionou@yahoo.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semi-classical ; Linear functionals ; Nonuniform lattice ; Classical orthogonal polynomials ; Semi-classical orthogonal polynomials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：819-836
• 全文大小：363 K

文摘

Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional 16302785&_mathId=si1.gif&_user=111111111&_pii=S0022247X16302785&_rdoc=1&_issn=0022247X&md5=2567d178f1b5a79dedf0dcf1c7e85f3a" title="Click to view the MathML source">L$\mathcal{L}$ are defined as polynomials 16302785&_mathId=si2.gif&_user=111111111&_pii=S0022247X16302785&_rdoc=1&_issn=0022247X&md5=ec3c9a45a3d48ca160280bc57c1aab98" title="Click to view the MathML source">(P_n)$(P_n)$ where the degree of 16302785&_mathId=si102.gif&_user=111111111&_pii=S0022247X16302785&_rdoc=1&_issn=0022247X&md5=0b2d9f69e9fda8cf3597cf3b1212b1b2" title="Click to view the MathML source">P_n$P_n$ is exactly n  , the 16302785&_mathId=si102.gif&_user=111111111&_pii=S0022247X16302785&_rdoc=1&_issn=0022247X&md5=0b2d9f69e9fda8cf3597cf3b1212b1b2" title="Click to view the MathML source">P_n$P_n$ satisfy the orthogonality relation and 16302785&_mathId=si1.gif&_user=111111111&_pii=S0022247X16302785&_rdoc=1&_issn=0022247X&md5=2567d178f1b5a79dedf0dcf1c7e85f3a" title="Click to view the MathML source">L$\mathcal{L}$ satisfies the Pearson equation where ϕ is a non zero polynomial and ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials.