Abstract
New generalization of Kravchenko–Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions is discussed. These functions are solutions of linear integral equations of special form. The spectrum of is a multiple infinite product of the spectra of atomic functions. dilated by the argument. Constructed generalized series has fast convergence. This property is confirmed by the presented truncation error bound formula and the results of a numerical experiment.
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