Fine spectra of the finite Hilbert transform in function spaces

Published 20 Dec 2019 in math.FA | (1912.09700v2)

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.

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