Spectral theory of multiplication operators on Hardy-Sobolev spaces

Abstract

For a pointwise multiplier $\phi$ of the Hardy-Sobolev space $H_{\beta }^2$ on the open unit ball $\bn$ in $\cn$, we study spectral properties of the multiplication operator $M_{\phi }:H_{\beta }^2\to H_{\beta }^2$. In particular, we compute the spectrum and essential spectrum of $M_{\phi }$ and develop the Fredholm theory for these operators.

24 pages