Multidimensional Inverse Problems for Differential Equations

absolutely integrable functions Akad belong boundary conditions CAUCHY data chapter coefficients consider const continuous function corresponding cosk Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution expression family of curves following theorem FOURIER transforms function u(r fundamental solution given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 18 integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inversion formula kernel L₁(D LAVRENT'EV linearized inverse problem mean values multidimensional inverse problems Nauk SSSR obtain operator L defined parameters polar potential theory problem for equation problem of determining Problems for Differential right-hand side ROMANOV second kind solution to equation take FOURIER transforms telegraph equation two-parameter family uniqueness theorem unit circle variables VOLTERRA equation waves αλ αξ αφ