Gravitation smoothing of time series (spectral properties)

This article continues the cycle of works by authors on the development of mathematical aspects methods of artificial intelligence for the processing of observations conducted under the guidance of academician A.D. Gvishiani, which was began in 2000. It is devoted to a new universal method of smoothing, originally intended for the analysis of geophysical time series. Gravitational smoothing formed the basis for studying the acceleration of the secular course of the Earth's main magnetic field with using of the observational data of the INTERMAGNET network. But the properties of the smoothing operator have not been studied so far. This aticle is first step to this goal.