Orthogonal polynomials associated with an inverse quadratic spectral transform

نویسندگان

  • Manuel Alfaro
  • Ana Peña
  • M. Luisa Rezola
  • Francisco Marcellán
چکیده

Let {Pn}n≥0 be a sequence of monic orthogonal polynomials with respect to a quasi–definite linear functional u and {Qn}n≥0 a sequence of polynomials defined by Qn(x) = Pn(x) + sn Pn−1(x) + tn Pn−2(x), n ≥ 1, with tn 6= 0 for n ≥ 2. We obtain a new characterization of the orthogonality of the sequence {Qn}n≥0 with respect to a linear functional v, in terms of the coefficients of a quadratic polynomial h such that h(x)v = u. We also study some cases in which the parameters sn and tn can be computed more easily, and give several examples. Finally, the interpretation of such a perturbation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is presented. AMS Subject Classification 2000: 42C05, 33C45.

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عنوان ژورنال:
  • Computers & Mathematics with Applications

دوره 61  شماره 

صفحات  -

تاریخ انتشار 2011