Spectral transformations and associated linear functionals of the first kind Articles uri icon

published in

publication date

  • June 2021

start page

  • 1

end page

  • 23


  • 2


  • 10

International Standard Serial Number (ISSN)

  • 2075-1680


  • Given a quasi-definite linear functional u in the linear space of polynomials with complex
    coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP
    in short) (Pn)n≥0. For a canonical Christoffel transformation ue = (x − c)u with SMOP (Pen)n≥0, we
    are interested to study the relation between ue and ug(1)
    , where u
    is the linear functional for the
    associated orthogonal polynomials of the first kind (P
    n )n≥0, and ug(1) = (x − c)u
    is its Christoffel
    transformation. This problem is also studied for canonical Geronimus transformations.


  • Mathematics


  • spectral transformation; darboux transformations; first kind orthogonal polynomials; laguerre-hahn linear functional