“…The Fourier theory of heat propagation had not been recognized for a long time; later on, this approach, referred to as harmonic Fourier analysis, got various applications (Fourier series and integrals, discrete transforms, fast discrete transforms) [5]; this theory was completed after J. Fourier, when D. Hilbert became an authoritative mathematician of that time (1862-1943). The direct integral Fourier transform maps a given continuous time function whose modulus is integrated on an infinite real time axis, to its spectral image as a function of the continuous frequency, also defined on the infinite real axis, [6]. Integral transforms and Fourier series are effectively used in various fields of physics and geometry, optics, number theory, combinatory, signal processing, probability theory, etc.…”