$E$ Type Singularities for Sufficiently Smooth Functions
Analysis of PDEs
2025-05-21 v1
Abstract
In this paper, we will consider -type singularities which are Arnol'd type. We provide invariant conditions for a sufficiently smooth functions to have singularities of type . We show the functions can be reduced to type normal form under some certain conditions. Moreover, we show that result on normal form for sufficiently smooth functions can be showed by the use of Implicit Function Theorem. The results can be utilized to investigate oscillatory integrals with sufficiently smooth phase function.
Keywords
Cite
@article{arxiv.2505.13939,
title = {$E$ Type Singularities for Sufficiently Smooth Functions},
author = {Ibrokhimbek Akramov and Dildora Ikromova},
journal= {arXiv preprint arXiv:2505.13939},
year = {2025}
}