On an inverse problem for a linear combination of orthogonal polynomials Articles uri icon

publication date

  • April 2014

start page

  • 570

end page

  • 585

issue

  • 4

volume

  • 20

international standard serial number (ISSN)

  • 1023-6198

electronic international standard serial number (EISSN)

  • 1563-5120

abstract

  • This paper deals with the analysis of the orthogonality of a monic polynomial sequence defined as a linear combination of a sequence of monic orthogonal polynomials withwhere for . Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials . We obtain the connection between the Jacobi matrices associated with and , respectively, by using an LU factorization. Some special cases of the above type relation are analysed.

keywords

  • orthogonal polynomials; inverse problems; linear functionals; jacobi matrices; functionals; sequences; intervals