Strong-linear independence for differential images of Gauss potentials

J. С. Mairhuber theorem concerning the Chebyshev approximation problem provides a resolution uniqueness only for the case of one-dimensional compacts. In present paper an attempt to overcome the above restriction by means of stochastic interpretation applied to solvability is taken. In the context of such a position the multiparametric system of Gauss potentials is studied. The strong linear independence for potentials and its images resulting from the constant factors linear differential operator is proved. The differentially conditioned analytic function generating based on a linear combination of Gauss potentials is examined.