ABOUT ONE OF THE PROBLEMS OF INTEGRAL GEOMETRY IN A STRIP ON A FAMILY OF BROKEN LINES - Uteuliev, N.U.; Djaykov, G.M.; Yadgarov, Sh.A. (FAN va JAMIYAT, 2019)
The article deals with the study of problems of integral geometry in a strip on a family of broken lines with a given weight function of a general form. The theorems of uniqueness and existence for the solution of the task are proved; an analytic representation of the solution in the class of smooth finite functions is obtained. An estimate of the solution of the task in Sobolev spaces is presented, from which its weak incorrectness follows. The obtained theoretical results are investigated by experimental data. The numerical and graphical results of applying these algorithms to the solution of the task are given. Such task have numerous applications in the mathematical study of the problems of seismic prospecting, the interpretation of geophysical and aerospace observations, in solving inverse task of astrophysics and hydro acoustics.