Spectral theory of multiplication operators on Hardy-Sobolev spaces

For a pointwise multiplier $varphi$ of the Hardy-Sobolev space $H^2_beta$ on the open unit ball $bn$ in $cn$, we study spectral properties of the multiplication operator $M_varphi: H^2_betato H^2_beta$. In particular, we compute the spectrum and essential spectrum of $M_varphi$ and develop the Fredholm theory for these operators.