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We prove here that under adequate restrictions, convergence of a sequence of vector-valued distributions {Pn} and boundedness of the sequence of their convolution inverses {Sn} implies convergence of {£„}; boundedness and convergence are formulated with respect to "fractional derivative norms" which include ordinary boundedness and convergence as a particular case. The results include diverse results for convergence of solutions of differential, difference and functional equations proved by Trotter, Kato, Goldstein, Ujishima, Ponomarev and others.

Convergence and approximation theorems for vector-valued distributions