Invariant Sums of Products of Differentials.

Based on the method proposed for solving the so-called -systems of linear equations, it is proved that the orders of homogeneous invariant differential operators of smooth real functions of one variable take values from to , and the dimension of the space of all such operators does not exceed . A classification of invariant differential operators of order is obtained for and for for all orders from 4 to 10. Homogeneous invariant differential operators of the smallest order and the largest order are given, respectively, by the product of the first differentials () and the Wronskian (). The existence of nonzero homogeneous invariant differential operators of order for is proved. [ABSTRACT FROM AUTHOR]