Fine spectra of the finite Hilbert transform in function spaces

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. (C) 2021 Elsevier Inc. All rights reserved.