Geronimus transformations of bivariate linear functionals Articles uri icon

publication date

  • April 2020

start page

  • 1

end page

  • 30

issue

  • 2(123736)

volume

  • 484

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

abstract

  • Given a linear functional u in the linear space of polynomials in two variables with real coefficients and a polynomial , in this contribution we deal with Geronimus transformations of u, i.e., those linear functionals v such that . The connection formulas between the sequences of bivariate orthogonal polynomials with respect to u and v are given. A matrix interpretation of such transformations by using LU and UL factorizations of the block Jacobi matrices associated with such polynomials is given. Finally, some illustrative examples of Geronimus transformations of weight function supported in domains of are discussed.

keywords

  • bivariate orthogonal polynomials; classical and semiclassical orthogonal polynomials