Paley-Wiener-Schwartz Theorems on Quadratic CR Manifolds

TL;DR

This paper extends Paley-Wiener-Schwartz theorems to quadratic CR manifolds, analyzing Schwartz functions and distributions on these complex geometric structures.

Contribution

It introduces new Paley-Wiener-Schwartz theorems specifically for quadratic CR manifolds, expanding the theoretical framework in complex analysis.

Findings

Established Paley-Wiener-Schwartz theorems for Schwartz functions on quadratic CR manifolds

Derived results for tempered distributions on these manifolds

Enhanced understanding of harmonic analysis in complex geometric contexts

Abstract

Given a quadratic CR manifold $\mathcal{M}$ embedded in a complex space, we study Paley-Wiener-Schwartz theorems for spaces of Schwartz functions and tempered distributions on $\mathcal{M}$.