New type Paley-Wiener theorems for the modified multidimensional Mellin transform (Q1271494)

The transmutation operator method is used in order to establish a relation between the support of a function \(f\in \mathbb{R}_+^n\) and the differentiability properties of its modified Mellin transform. The analogous result for the inverse Mellin transform is also obtained. The theorems are real variable results which do not require estimations in the complex domain. Further the results are not restricted to only bounded or convex supports.