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Jacobi Block Matrices with Constant Matrix Terms

  • Marcin J. Zygmunt
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 154)

Abstract

We investigate a solution of the difference equation
$$tU_n^{A,B}(t) = AU_{n + 1}^{A,B}(t) + BU_n^{A,B}(t) + AU_{n - 1}^{A,B}(t)$$
with the boundary conditions U 0 A,B , where A, B are hermitian matrices. U n A,B , are usually called matrix Chebyshev polynomials of the second kind. The above equation cannot be easily simplified as in scalar case because A and B do not need to commute. However we are able to compute spectrum of the corresponding orthogonality measure which is very important to investigate discrete Schrödinger operator related to U n A,B .

Keywords

Chebyshev polynomials discrete Schrodinger operator Jacobi block-matrices matrix orthogonal polynomials 

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Marcin J. Zygmunt
    • 1
    • 2
  1. 1.Institute of MathematicsUniversity of WroclawWroclawPoland
  2. 2.Institute of MathematicsWroclaw University of TechnologyWroclawPoland

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