Multiple Geronimus transformations Articles uri icon

publication date

  • August 2014

start page

  • 158

end page

  • 183

volume

  • 454

international standard serial number (ISSN)

  • 0024-3795

electronic international standard serial number (EISSN)

  • 1873-1856

abstract

  • We consider multiple Geronimus transformations and show that they lead to discrete (non-diagonal) Sobolev type inner products. Moreover, it is shown that every discrete Sobolev inner product can be obtained as a multiple Geronimus transformation. A connection with Geronimus spectral transformations for matrix orthogonal polynomials is also considered.

keywords

  • band matrix; cholesky decomposition; geronimus transformation; jacobi matrix; orthogonal polynomials; sobolev inner products; jacobian matrices; orthogonal functions; band matrix; cholesky decomposition; geronimus transformation; jacobi matrix; orthogonal polynomial; sobolev inner products; linear transformations