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Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for $L^2$-harmonic forms

Bent Orsted·Genkai Zhang
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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 $C^n$. We prove that Szegö map is a unitary operator from a subspace of $(p, q-1)$-forms on the sphere defined by the Tanaka operators and the normal vector field onto the space of $L^2$-harmonic $(p, q)$-forms on the unit ball. Our results generalize earlier result of Folland.

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BibTeXRIS

Bent Orsted, Genkai Zhang. 2004-12-01. Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for $L^2$-harmonic forms. https://arxiv.org/abs/math/0412017

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