Integral transforms by green's function on rⁿ

Abstract

For and for nonnegative integersWe set

Let be the linear partial differential operator of order m satisfying p(ξ) ≠ 0 for all ξ ε Rⁿ. Then, for the uniquely determined tempered fundamental solution , we consider the integral transform

and investigate the relationship between f and u. In particular, we establish some isometrical identities and inverse formulae between f and u for functions f ε L₂(Rⁿ).