A questionable publication of T.I. Savyolova is analysed. The paper claims, that it is possible to determine Ph(y) pole figure values for y∈Y(h;h0,Y0) using only data from y∈Y0 of a single pole figure Ph0(y). The contradiction to the common knowledge can be resolved well understanding that there is a general difference between the term solutions
(or continuation of solutions) of an ultrahyperbolic equation (satisfied by the axis distribution function A(h, y)) and the term pole figure. Pole figures considered in texture analysis are two-dimensional projections of a three-dimensional object (the ODF f(g)). For limited data sets the equation ΔhA(h,y)=ΔyA(h,y) bears only a necessary, but not sufficient character in order to get solutions of interest, i.e. it cannot be guaranteed that a h-specific continuation of a starting solution Ph0(y) will be a “h-projection” of the same ODF, which belongs to a concrete sample and possesses the “h0-projection” Ph0(y).Consequently, to name such a h-specific continuation “pole figure” is incorrect. The consideration of formal (unambiguous only by artificial conditions) continuations of solutions may be mathematically interesting, but is of no practical importance for texture analysis. Examples (already considered by the authors about twenty years ago) are given, how to construct in a much more simple way continuations of solutions of the same useless type like in the paper under discussion.
