Stratified reduction of singularities of generalized analytic functions

Abstract

Generalized analytic functions are naturally defined in manifolds with boundary and are built from sums of convergent real power series with non-negative real exponents. In this paper we deal with the problem of reduction of singularities of these functions. Namely, we prove that a germ of generalized analytic function can be transformed by a finite sequence of blowing-ups into a function which is locally of monomial type with respect to the coordinates defining the boundary of the manifold where it is defined.