Jacobi Block Matrices with Constant Matrix Terms
Marcin J. Zygmunt · Birkhäuser Basel eBooks · 2004
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 , where A, B are hermitian matrices. U , 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 .