Convergence and approximation theorems for vector-valued distributions

Hector O. Fattorini

Vol. 105 (1983), No. 1, 77–114

DOI: 10.2140/pjm.1983.105.77

Abstract

We prove here that under adequate restrictions, convergence of a sequence of vector-valued distributions {P_n} and boundedness of the sequence of their convolution inverses {S_n} implies convergence of {S_n}; 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.

Mathematical Subject Classification 2000

Primary: 46F10

Secondary: 47D05

Milestones

Received: 29 June 1981

Published: 1 March 1983