(M,N)-Coherent pairs of linear functionals and Jacobi matrices

Francisco Marcellán and Natalia Camila Pinzón-Cortés

Applied Mathematics and Computation, 2014, vol. 232, issue C, 76-83

Abstract: A pair of regular linear functionals (U,V) in the linear space of polynomials with complex coefficients is said to be an (M,N)-coherent pair of order m if their corresponding sequences of monic orthogonal polynomials {Pn(x)}n⩾0 and {Qn(x)}n⩾0 satisfy a structure relation∑i=0Mai,nPn+m-i(m)(x)=∑i=0Nbi,nQn-i(x),n⩾0,where M,N, and m are non-negative integers, {ai,n}n⩾0,0⩽i⩽M, and {bi,n}n⩾0,0⩽i⩽N, are sequences of complex numbers such that aM,n≠0 if n⩾M,bN,n≠0 if n⩾N, and ai,n=bi,n=0 if i>n. When m=1,(U,V) is called an (M,N)-coherent pair.

Keywords: Coherent pairs; Structure relations; Regular linear functionals; Orthogonal polynomials; Classical orthogonal polynomials; Sobolev orthogonal polynomials; Monic Jacobi matrix (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:76-83

DOI: 10.1016/j.amc.2014.01.055

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