A note on the Geronimus transformation and Sobolev orthogonal polynomials Articles uri icon

publication date

  • October 2014

start page

  • 271

end page

  • 287

issue

  • 2

volume

  • 67

international standard serial number (ISSN)

  • 1017-1398

electronic international standard serial number (EISSN)

  • 1572-9265

abstract

  • In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.

keywords

  • orthogonal polynomials; geronimus transformation; sobolev inner products; cholesky decomposition; jacobi matrices