Recent trends on analytic properties of matrix orthonormal polynomials.
We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.
We prove F. Riesz’ inequality assuming the boundedness of the norm of the first arithmetic mean of the functions with p ≥ 2 instead of boundedness of the functions φₙ of an orthonormal system.