Multidimensional Inverse Problems for Differential Equations

absolutely integrable functions analytic function belong boundary conditions CAUCHY data chapter consider const continuous function corresponding cosk Denote derive determining a function differential equation domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function u(M,M,t function u(r function x1,x fundamental solution G₂ given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 16 integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inverse problem inversion formula kernel L₁(D linearized inverse problem M₁ mean values multidimensional inverse problems obtain operator L defined parameters polar problem for equation problem of determining R₁ right-hand side second kind solution to equation take FOURIER transforms telegraph equation travel-times two-parameter family u₁ M,M,t unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation w₂