Journal of Operator Theory

Volume 93, Issue 2, Spring 2025 pp. 541-568.

On the continuous spectra of Toeplitz operators with pluriharmonic symbols

Authors: Jingbo Xia
Author institution: College of Data Science, Jiaxing University, Jiaxing 314001, China \textit{and} Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.

Summary: We show that certain self-adjoint Toeplitz operators on the Hardy space of the unit sphere have purely absolutely continuous spectrum. For a subclass of these operators, we show that the spectral multiplicity function is not locally $L^1$.

DOI: http://dx.doi.org/10.7900/jot.2023jun25.2429
Keywords: Toeplitz operator, absolutely continuous spectrum

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