Abstract

We consider the problem of finding \(u\in L^2(I)\), \(I = (0,1)^2\subset\mathbb R^2\), satisfying \[ \int_I u(x,y)x^{\alpha_k} y^{\alpha_l} dx dy =\mu_{kl}, \] where \(k,l = 0,1,2,\dots,(\alpha_k)\) is a sequence of pairwise distinct real numbers which are greater than \(-1/2\), and \(\mu=(\mu_{kl})\) is a given bounded sequence of real numbers. This is an ill-posed problem. We regularize the problem by finite moments and then apply the result to reconstruct a function from a sequence of its Laplace transforms.