AN EXACT INNER STRUCTURE OF THE BLOCK JACOBI-TYPE UNITARY MATRICES CONNECTED WITH THE CORRESPONDING DIRECT AND INVERSE SPECTRAL PROBLEMS
Mykola E. Dudkin · 2008
Dedicated to Myroslav Lvovych Gorbachuk on the occasion of his 70th birthday. Abstract. We discuss a problem posed by M. J. Cantero, L. Moral, and L. Velázquez about representing an arbitrary unitary operator with a CMV-matrix. We consider this problem from the point of view of a one-to-one correspondence between a non-finite unitary operator and an infinite (five-diagonal) block three-diagonal Jacobi-type matrix in the form of the corresponding direct and inverse spectral problems for the trigonometric moment problem. Since the earlier obtained block three-diagonal Jacobi-type unitary matrix has not been fully described, we continue this investiga-tions in the present article. In particular, we show that this exact inner structure coincides with an earlier obtained CMV-matrix. 1.