Application of Laguerre polynomials to invert a semi-infinite convolution

We propose a spectral method of inverting one- and two-dimensional semi-infinite convolutions using the Laguerre polynomials. We construct systems of linear algebraic equations to determine the coefficients of the corresponding Fourier-Laguerre series. We analyze the computational error in the coefficients of the orthogonal series that arise as a result of errors in the data. Applying the Laguerre polynomials makes it possible to eliminate the discretization procedure, which may take the solution of the perturbed equation outside the region of well-posedness.