Weyl–Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle

We provide a detailed treatment of Weyl–Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions, variants of Weyl–Titchmarsh functions, and Green's functions. In particular, we discuss the corresponding spectral representations of half-lattice and full-lattice CMV operators.