Abstract:
In this paper we consider the possibility of building the Hilbert space by completion of the unitary space generated by the fractional differentiation operator. A method of constructing this space is similar to [1, c. 44] but at the same time, is more general in a certain sense because a weighting function is present in the bilinear form. The embedding theorem for the constructed Hilbert space in the weighted Lebesgue space of square integrable functions is proved. The consequence of this theorem is the appropriate equipment of the weighted Lebesgue space of square integrable functions in the sense of [8, p. 47].
