Exact Fourier inversion formula over manifolds
Nefton Pali
TL;DR
This paper presents an exact Fourier inversion formula for differential operators on Riemannian manifolds, offering a coordinate-free approach that advances the theoretical understanding of pseudo-differential operators.
Contribution
It introduces an exact, coordinate-free Fourier inversion formula for differential operators on manifolds, enhancing the theoretical framework of pseudo-differential operators.
Findings
Provides an exact Fourier inversion formula without smooth error terms
Offers a coordinate-free approach to pseudo-differential operator theory
Advances the mathematical understanding of differential operators on manifolds
Abstract
We show an exact (i.e. no smooth error terms) Fourier inversion type formula for differential operators over Riemannian manifolds. This provides a coordinate free approach for the theory of pseudo-differential operators.
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