AbstractS. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see 5; Goel discussed some special cases earlier in 1969; see also 1, 4, 6). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see 1 ).This paper is devoted to the investigation of A‐minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g‐continuity of these splines. The application of these results to polynomial splines ofm‐th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of theiri‐th derivative (i= 1, ⃛,m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less thani). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one‐to‐one‐correspondence with certain planes contai
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