Fine spectra of the finite Hilbert transform in function spaces

2019/12/20 by Guillermo P. Curbera, Curbera, Guillermo P., Susumu Okada +3
Mathematics · #46E30 #47B34 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 44A15 #Secondary 47A53 #math.FA #msc:44A15 #msc:46E30 #msc:47A53 #msc:47B34

paper · pdf · doi:10.48550/arxiv.1912.09700

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

arxiv created 2021/01/14 · arxiv updated 2021/01/15

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.

Related

• Non-extendability of the finite Hilbert transform
• Measure theoretic aspects of the finite Hilbert transform
• The finite Hilbert transform acting in the Zygmund space LlogL
• Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis
• The Hilbert transform, rearrangements, and logarithmic determinants