The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Revista Matemática Iberoamericana


Full-Text PDF (1420 KB) | Metadata | Table of Contents | RMI summary
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.

No keywords available for this article.

Böttcher Albrecht, Spitkovsky Ilya: Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weight. Rev. Mat. Iberoam. 9 (1993), 257-279. doi: 10.4171/RMI/136