Observability from a measurable set for functions in a Gevrey class

TL;DR

This paper establishes observability inequalities for Gevrey class functions and sums of Laplace eigenfunctions on Riemannian manifolds, with explicit eigenvalue dependence, advancing control theory in geometric analysis.

Contribution

It introduces a new observability inequality for Gevrey functions from measurable sets and applies it to eigenfunction sums on Riemannian manifolds, providing explicit eigenvalue dependence.

Findings

Observable estimates for Gevrey functions from measurable sets

Explicit eigenvalue dependence in observability estimates

Application to sums of Laplace eigenfunctions on manifolds

Abstract

We provide an observability inequality in terms of a measurable set for general Gevrey regular functions. As an application, we establish an observability estimate from a measurable set for sums of Laplace eigenfunctions in a compact and connected boundaryless Riemannian manifold that belongs to the Gevrey class. The estimate has an explicit dependence on the maximal eigenvalue.