JournalsrmiVol. 9, No. 2pp. 257–279

Wiener-Hopf integral operators with PCPC symbols on spaces with Muckenhoupt weight

  • Albrecht Böttcher

    Technische Universität Chemnitz, Germany
  • Ilya Spitkovsky

    The College of William and Mary, Williamsburg, USA
Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weight cover
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Abstract

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 LP(R+,ω)L^P (\mathbb R_+, \omega) with a Muckenhoupt weight ω\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 pp and the behavior of the weight ω\omega at the origin and at infinity.

Cite this article

Albrecht Böttcher, Ilya Spitkovsky, Wiener-Hopf integral operators with PCPC symbols on spaces with Muckenhoupt weight. Rev. Mat. Iberoam. 9 (1993), no. 2, pp. 257–279

DOI 10.4171/RMI/136