Revista Matemática Iberoamericana
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Published online: 1993-08-31
Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weightAlbrecht Böttcher and Ilya Spitkovsky (1) Technische Universität Chemnitz, Germany
(2) The College of William and Mary, Williamsburg, USA
We describe the spectrum and the essential spectrum and give an index formula for Wiener-Hopf integral operators with piecewise continuous symbols on the space $L^P (\mathbb R_+, \omega)$ with a Muckenhoupt weight $\omega$. Our main result says that the essential spectrum is a set resulting from the essential range of the symbol by joining the two endpoints of each jump by a certain sickle-shaped domain, whose shape is completely determined by the value of $p$ and the behavior of the weight $\omega$ at the origin and at infinity.
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Böttcher Albrecht, Spitkovsky Ilya: Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weight. Rev. Mat. Iberoamericana 9 (1993), 257-279. doi: 10.4171/RMI/136