Gyrya N. Distribution of values of holomorphic almost periodic functions of several variables

It is described a relation between the P-indicator and the supporting function of the spectrum for almost periodic functions. Also, it has been found a connection between Jessen's function and the P-indicator for almost periodic functions of many variables. As a consequence we obtain the multidimensional analogues of the Sohotsky-Weierstrass theorem and the Picard theorem. Then, the multidimensional analogue of mean motion has been introduced. It has been proved that its asymptotical behavior is just the gradient of the supporting function of the spectrum. We found in finite dimensional space a criterium for the spectrum of an almost periodic in the sense of Besicovitch function to lie in some cone. If this function has a holomorphic and bounded in the Besicovitch's metric extension in some cone than its spectrum is contained in some conjugate cone.