On the operation of composition of distributions

On the distributional compositions of functions and distributions

“…We try to formulate earlier results in a more general setting and correct inaccuracies in our previous papers [2,3,7]. We expose the role of various classes of delta-sequences and measure theoretical techniques used in [7] to show how nicely they work in the subject of distributional compositions.…”

“…Independently, the second and the third authors used in [7] other techniques to omit difficulties in the proofs and generalize some theorems from [2]. In particular, there appeared a possibility (not used in [7] yet) of extension of the results to wider classes of delta-sequences.…”

“…In particular, there appeared a possibility (not used in [7] yet) of extension of the results to wider classes of delta-sequences.…”

“…Moreover, we collect some earlier and new results on distributional compositions in Section 3 for functions and in Section 4 for distributions, given mostly for wider classes of delta-sequences than the class 1 + (see Section 2) considered before (see [2,3,7]). At the end of Section 4 (Example 4.6), we conclude from Theorem 4.5 proved in [2,3] several formulas, more general than ones given in [3], with the Dirac delta distribution δ.…”

“…We expose the role of various classes of delta-sequences and measure theoretical techniques used in [7] to show how nicely they work in the subject of distributional compositions.…”