A direct energy estimates for effectively hyperbolic operators

TL;DR

This paper presents a simplified method for deriving energy estimates for effectively hyperbolic operators, avoiding complex Fourier integral operators and utilizing Weyl calculus with multiple metrics for efficiency.

Contribution

It introduces a more straightforward approach to energy estimates for hyperbolic operators, leveraging Weyl calculus and multiple metrics, reducing complexity compared to prior methods.

Findings

Simplified derivation of energy estimates

Avoidance of Fourier integral operators

Efficient use of Weyl calculus with multiple metrics

Abstract

This paper is devoted to a simpler derivation of energy estimates compared to previously existing ones, for effectively hyperbolic operators. One of main points is no use of general Fourier integral operators and another point is an efficient use of Weyl calculus of pseudodifferential operators associated with several different metrics.