An orthonormal basis functions method for moment problems

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In this paper, a new computational method is developed to recover an unknown function from its moments with respect to general kernel functions. By using the Gram–Schmidt orthonormalization technique, our method is shown to be efficient and can be interpreted as a generalization of the Talenti method. Convergence and error estimates are also discussed. For the purposes of verification and application, the method is applied to solve both Cauchy problem for Laplace equation and a Fredholm integral equation of the first kind.