Spectral criteria of abstract functions; integral and difference problems (Q1267372)

The authors resolve a difference problem for certain classes \(M\) of functions from \(C_{ub} (J,X)\), with \(J\in \{R^+,R\}\). In particular they show that if \(\varphi\in M\) then its indefinite integral \(P \varphi\in M\) satisfies certain conditions. The authors also extend a theorem of Loomis to large classes of functions from \(C_{ub}(\mathbb{R},X)\).