The wave front set of oscillatory integrals with inhomogeneous phase function

TL;DR

This paper introduces a generalized framework for oscillatory integrals with inhomogeneous phase functions of arbitrary positive order and characterizes their wave front sets, extending classical results for homogeneous phases.

Contribution

It generalizes the concept of oscillatory integrals to include inhomogeneous phases and provides a new characterization of their wave front sets.

Findings

Wave front set characterization for inhomogeneous phase functions

Extension of classical results to arbitrary positive order phases

Framework applicable to broader classes of oscillatory integrals

Abstract

A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the well-known result for phase functions that are homogeneous of order one.