# Resolvent estimates related with a class of dispersive equations

## TL;DR

This paper provides a straightforward proof of resolvent estimates for elliptic Fourier multipliers and applies these results to analyze smoothing effects in certain dispersive equations, focusing on Fourier transform restrictions.

## Contribution

It introduces a simple proof technique for resolvent estimates and applies it to dispersive equations, enhancing understanding of smoothing phenomena.

## Key findings

- Resolved resolvent estimates for elliptic Fourier multipliers
- Established smoothing estimates for dispersive equations
- Analyzed Fourier transform restrictions on cotangent spheres

## Abstract

We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.