Cks-space in Terms of Growth Functions

A class of growth functions u is introduced to construct Hida distributions and test functions. The Legendre transform lu of u is used to define a sequence α(n) = (lu(n)n!), n ≥ 0, of positive numbers. From this sequence we get a CKS-space. Under various conditions on u we show that the associated sequence {α(n)} satisfies those conditions for carrying out the white noise distribution theory on the CKS-space. We show that u and its dual Legendre transform u∗ are growth functions for test and generalized functions, respectively, in the characterization theorems.