Generalized Chebyshev polynomials and discrete Schrödinger operators
Marcin J. Zygmunt · Journal of Physics A Mathematical and General · 2001
We investigate a solution of the difference equation with the boundary conditions U 0 A , B = I , U -1 A , B = 0, where A , B are Hermitian elements of a C *-algebra. U n A , B are usually called generalized Chebyshev polynomials of the second kind. The equation (⋆) cannot be easily simplified as in the scalar case because A and B do not need to commute. However, we are able to compute the spectrum of the corresponding orthogonality measure which is very important for the investigation of the discrete Schrödinger operator related to U n A , B .