MORERA-TYPE THEOREM IN THE UNIT CIRCLE

New generalizations of the Morera function holomorphy theorem have been obtained. The precise conditions of growth of ? ∈C(H2) under which the boundary of a hyperbolic rectangle, or the boundary of a hyperbolic quadrangle act as the Morera set for the group of transitions of the NA hyperbolic plane H2 have been determined. The cases of two hyperbolic rectangles and two hyperbolic quadrangles have also been considered. Examples of functions with zero integrals on borders of hyperbolic rectangles and functions with zero integrals on borders of hyperbolic quadrangles, confirming the accuracy of conditions acquired.