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

Albrecht Böttcher, Ilya M. Spitkovsky (1993)

Revista Matemática Iberoamericana

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) with a Muckenhoupt weight ω. 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 ω at the origin and at infinity.

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