The paper is a review of certain existence theorems concerning the convolution of functions, distributions, and ultradistributions of Beurling type with supports satisfying suitable compatibility conditions. The fact that some conditions are essential for the existence of the convolution in the discussed spaces follows from earlier results and the proofs given at the end of this paper.

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We consider several general sequential conditions for convolvability of two Roumieu ultradistributions on R d in the space D ′{Mp} and prove that they are equivalent to the convolvability of these ultradistributions in the sense of Pilipović and Prangoski. The discussed conditions, based on two classes U {Mp} and U {Mp} of approximate units and corresponding sequential conditions of integrability of Roumieu ultradistributions, are analogous to the known convolvability conditions in the space D ′ of distributions and in the space D ′(Mp) of ultradistributions of Beurling type. Moreover, the following property of the convolution and ultradifferential operator P (D) of class {M p } is proved: if S, T ∈ D ′{Mp} (R d ) are convolvable, then P (D)(S * T ) = (P (D)S) * T = S * (P (D)T ).

We consider several general conditions for integrability of two Roumieu ultradistributions on R d in the space D ′{Mp} and prove their equivalence. The discussed sequential conditions are based on two classes U {Mp} and U {Mp} of approximate units and allow one to introduce sequential definitions of the convolution in D ′{Mp} , analogous to the known definitions in the space D ′ of distributions and in the space D ′(Mp) of ultradistributions of Beurling type.