Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2（а↓Ω）. In addition, the characteristic equation of analytic Toeplitz operators iааs obtained.
In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces. In addition,the spectrum theorem is obtained for some special multiplier.
