Asymptotic expansion of oscillatory integrals with singular phases

TL;DR

This paper analyzes the singularities of one-dimensional oscillatory integrals with singular phases, providing asymptotic expansions and extending results to Laplace integrals, enhancing understanding of their behavior near singularities.

Contribution

It introduces a detailed asymptotic expansion framework for oscillatory integrals with singular phases, including Laplace integrals, which was not previously well-understood.

Findings

Derived asymptotic expansions for integrals with singular phases

Extended analysis to Laplace integrals with similar singularities

Provided a comprehensive description of singularities in oscillatory integrals

Abstract

The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result is also given.