Representations of inverse functions

Abstract

Let ϕ : E ^ → E \phi : \hat E \rightarrow E be an arbitrary map from an abstract set E ^ \hat E into an abstract set E E . We shall use the theory of reproducing kernels to provide a general method for representing the inverse map ϕ − 1 \phi ^{-1} in terms of ϕ \phi . We give several concrete examples of this method.