Abstract
An analogue of the Fourier integral with respect to a generalized multiplicative system of functions is constructed. It is proved that every absolutely integrable andg-continuous function can be represented as such a multiplicative Fourier integral. The multiplicative Fourier transformation (the spectral function of the multiplicative Fourier integral) is introduced, and the direct and inverse discrete multiplicative Fourier transformations are constructed. The relationship between the spectral function of the multiplicative Fourier integral and the discrete multiplicative Fourier transformation is illuminated. This enables us to elucidate the influence of the discretization of a given function on the properties of its multiplicative spectral characteristics.
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