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

Author

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  • Marcellán, Francisco
  • Pinzón-Cortés, Natalia Camila

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.

Suggested Citation

  • Marcellán, Francisco & Pinzón-Cortés, Natalia Camila, 2014. "(M,N)-Coherent pairs of linear functionals and Jacobi matrices," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 76-83.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:76-83
    DOI: 10.1016/j.amc.2014.01.055
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