Spectral synthesis for the differentiation operator in the Schwartz space

TL;DR

This paper investigates the spectral synthesis problem for the differentiation operator in the Schwartz space and explores the local structure of submodules in a related entire functions module.

Contribution

It provides a new analysis of spectral synthesis for the differentiation operator in Schwartz space and characterizes submodules in a specific entire functions module.

Findings

Spectral synthesis results for the differentiation operator in Schwartz space.

Characterization of closed submodules in a module of entire functions.

Insights into the structure of the dual problem for local descriptions.

Abstract

We consider the spectral synthesis problem for the differentiation operator D=d/dt in the Schwartz space E(a;b) and the dual problem of local description for closed submodules in a special module of entire functions.