Laplacians on quotients of Cauchy-Riemann complexes and Szeg\"o map for $L^2$-harmonic forms
Representation Theory
2007-05-23 v1 Complex Variables
Abstract
We compute the spectra of the Tanaka type Laplacians on the Rumin complex, a quotient of the tangential Cauchy-Riemann complex on the unit sphere in . We prove that Szeg\"o map is a unitary operator from a subspace of -forms on the sphere defined by the Tanaka operators and the normal vector field onto the space of -harmonic -forms on the unit ball. Our results generalize earlier result of Folland.
Keywords
Cite
@article{arxiv.math/0412017,
title = {Laplacians on quotients of Cauchy-Riemann complexes and Szeg\"o map for $L^2$-harmonic forms},
author = {Bent Orsted and Genkai Zhang},
journal= {arXiv preprint arXiv:math/0412017},
year = {2007}
}