Two classes of weakly ill-posed problems of integral geometry on the plane (Q1921774)

The paper contains a uniqueness theorem for the integral equation \[ \int^{x+\sqrt y}_{x-\sqrt y} g(x,\xi)u \bigl(\xi,y-(x-\xi)^2\bigr) d\xi+\int^y_0\int^{x+h}_{x-h} K(x,y, \xi, \eta)u(\xi,\eta)d\xi d\eta={\mathcal F}(x,y), \] where \(h= \sqrt{y-\eta}\) and \(g(x,\xi) = \text{sgn} (x-\xi)\) or \(g(x,\xi)=|x-\xi|\).