On Fundamental Properties of Direct Correspondence Operators in Defining Star-Shaped Domains, Similar to Required Domains

It is shown that direct correspondence operators in the problems of defining star-shaped domains similar to the given ones are linear, limited, continuous and compact in the space of the functions most frequently used in solving inverse problems of potential. The authors carried out spectral analysis of the operators and, on its basis, indicated effective applicable criteria for the output data and the solutions for the appropriate range of operator values, as well as definition areas for normal solutions.