Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for L²-harmonic forms

الأصل · EN

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 Cⁿ. 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 L²-harmonic (p, q)-forms on the unit ball. Our results generalize earlier result of Folland.