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An inverse problem of the theory of the electromagnetic radiation for a function spectrum with a finite number of zeros

The radiation energy of an electromagnetic field in a certain frequency interval is proportional to the square of the modulus of the Fourier transform of this field. The determination of the radiation energy is a direct problem and has an independent value in solving many problems of radiation theory. It is of great 
interest, according to the known spectrum of the energy distribution of radiation over frequencies, to find the function of the electromagnetic field that created this spectrum, i.e. solve the inverse problem of radiation theory. In this paper, the above inverse problem is solved, namely, the function of the electromagnetic field is sought from a known function of the spectrum having a finite number of zeros on the frequency interval.