$L^2$ -调和形式的Cauchy-Riemann复形和Szegö映射上的Laplacian
Laplacians on quotients of Cauchy-Riemann complexes and Szegö map for $L^2$-harmonic forms
摘要：
我们计算了$C^n$中单位球面上切向Cauchy-Riemann复形的商Rumin复形上的Tanaka型Laplacian的谱。证明了Szegö映射是从Tanaka算子所定义的球面上的$(p, q-1)$ -形式的子空间到单位球上的$L^2$ -调和$(p, q)$ -形式的空间的酉算子.我们的结果推广了Folland的早期结果。
英文摘要：
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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