On an inverse problem for a linear combination of orthogonal polynomials

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Marcellan F., VARMA S.

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, cilt.20, sa.4, ss.570-585, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/10236198.2013.864287
  • Dergi Adı: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.570-585
  • Anahtar Kelimeler: orthogonal polynomials, inverse problems, linear functionals, Jacobi matrices, INTERVALS
  • Ankara Üniversitesi Adresli: Evet

Özet

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.