6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Marcin Zygmunt

Spectral Analysis of Block Jacobi Matrices with Singular Entries

Three-diagonal block matrices (BM) are strictly connected with matrix-valued orthogonal polynomials (MOP).
Methods arising from the theory of those MOP gives answers to questions about spectrum of corresponding BM.

The case of singular coefficients in matrix-valued three-term recurrence formula such MOP satisfy will be treated.
The results will be applied to give another approach to the analysis of classic orthogonal polynomials satisfying three-term recurrence formula with periodic coefficients.

  1. M. J. Zygmunt: Matrix orthogonal polynomials and continued fractions, Linear Alg. Appl., 340 1-3 (2002), 155-168.
  2. M. J. Zygmunt: Jacobi Block Matrices with Constant Matrix Terms, Oper. Theory: Adv. & Appl., 154 (2004), 233-238.
  3. M. J. Zygmunt: Matrix orthogonal polynomials with respect to a non-symmetric matrix of measures, Opuscula Math., 36 3 (2016), 409-423.
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