On the Fourier transform of dominated mappings

Boolean Valued Analysis

“…In particular, D(G, Y C ) is a Dedekind complete complex vector lattice. (2) Kusraev and Malyugin in [24] abstracted Takeuti's results in the following directions: First, they considered more general arrival spaces, namely, norm complete lattice normed spaces. So the important particular cases of Banach spaces and Dedekind complete vector lattices were covered.…”

“…In particular, Theorem 5.12 and Corollary 5.13 correspond to [24, Theorem 4.3] and [24,Theorem 4.4]; while their lattice normed versions, to [24,Theorem 4.1] and [24,Theorem 4.5], respectively.…”

“…Proposition 3.3 in Takeuti [37] is essentially the same result for the particular departure and arrival spaces; i.e., X = L 1 (G) and Y = (B). Theorem 5.11 is taken from Kusraev and Malyugin [24]. In the case of Q compact, it was proved by Wright in [44,Theorem 4.1].…”