In the recent paper [3] by Asai et al., the growth order of holomorphic functions on a nuclear space has been considered. For this purpose, certain classes of growth functions u are introduced and many properties of Legendre transform of such functions are investigated. In [4], applying Legendre transform of u under the conditions (U0), (U2) and (U3) (see §2), the Gel’fand triple [E ]u ⊂ (L) ⊂ ...