Solution to integral equations with $\delta$-like kernel

The subject of consideration is the integral equations with $\delta$-like kernel which result from the processing of physical process spectra, in the impulse technique, as well as in the time series analysis. Solution and estimates of the integral equations by the Gaussian or the Legendre least squares methods and by their regularized forms, like the orthogonal projections method, are well known. Here, contrary to the mentioned methods, the analysis focuses on the form of the least-squares method which uses the integral function theory, when the spectrum and length of the function are in the uncertainty principle relation.