Laplacians on Quotients of Cauchy-riemann Complexes and Szegö Map for L-harmonic Forms
نویسنده
چکیده
We compute the spectra of the Tanaka type Laplacians = ∂̄ Q∂̄Q + ∂̄Q∂̄ ∗ Q and △ = ∂ ∗ Q∂Q+ ∂Q∂ ∗ Q on the Rumin complex Q, a quotient of the tangential Cauchy-Riemann complex on the unit sphere S in Cn. We prove that Szegö map is a unitary operator from a subspace of (p, q− 1)-forms on the sphere defined by the operators △ and the normal vector field onto the space of L-harmonic (p, q)-forms on the unit ball. Our results generalize earlier result of Folland.
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