Fine spectra of the finite Hilbert transform in function spaces

Abstract

We investigate the spectrum and fine spectra of the finite Hilbert transform acting on rearrangement invariant spaces over $(-1,1)$ with non-trivial Boyd indices, thereby extending Widom's results for $L^p$ spaces. In the case when these indices coincide, a full description of the spectrum and fine spectra is given.

26 pages, 1 figure. Minor changes from previous version. This is the final version, to be published in Advances in Mathematics