Multidimensional Inverse Problems for Differential Equations

absolutely integrable functions analytic function arbitrary belong boundary conditions CAUCHY data chapter consider const continuous function corresponding Denote derive determining a function differential equation domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function u(r fundamental solution given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inverse problem inversion formula kernel L₁ linearized inverse problem M₁ mean values multidimensional inverse problems n₁ obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₁ R₂ relations right-hand side second kind SM,t 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 waves wxxx θε ду эф