The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials

We study the operator moment problem for a (p + 2)-diagonal nonsymmetric matrix operator and give an explicit form of the Favard theorem for vector orthogonal polynomials. As a main tool we use the development of a system of resolvent functions of the operator in a vector continued fraction by a modified Jacobi-Perron algorithm.