Resolvent Means and Inverting Generalized Fourier Transforms

摘要

In proving summability the fact that the resolvent kernel has properties analogous to those of certain L superscript 1-radially decreasing convolution kernels. A classical solution to the pointwise evaluation of an inverse Fourier transform is to apply summability methods. In experiments which give the coefficients of eigenfunctions expansions, measuring errors cause small perturbations in the expansion coefficients. Thus stable summability methods which recover from the perturbed expansion a good approximation to the original function f, at points where f is sufficiently regular, are of interest.