A Study on the Pointwise Time-Space Estimates of Fundamental Solution for Higher Order Schr\odinger Equation Whose Symbol Function is One Kind of Degenerate Polynomial

TL;DR

This paper investigates pointwise time-space estimates for the fundamental solution of higher order Schrödinger equations with degenerate polynomial symbols, improving and generalizing previous results.

Contribution

It provides enhanced estimates for the fundamental solution, extending prior work to more general degenerate polynomial symbols.

Findings

Improved pointwise estimates for fundamental solutions.

Generalization of previous results to broader classes of polynomial symbols.

Enhanced understanding of the behavior of higher order Schrödinger equations.

Abstract

In this paper we investigated the point-wise time-space estimates of the fundamental solution for higher order Schr\"odinger equation. These estimates improve the result of Yao [2] and generalize the one of Cui [1].