Revista Matemática Iberoamericana


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Volume 9, Issue 2, 1993, pp. 257–279
DOI: 10.4171/RMI/136

Published online: 1993-08-31

Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weight

Albrecht Böttcher[1] and Ilya Spitkovsky[2]

(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