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Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

A. BöttcherM. Seybold — 2000

Studia Mathematica

The discrete Wiener-Hopf operator generated by a function a ( e i θ ) with the Fourier series n a n e i n θ is the operator T(a) induced by the Toeplitz matrix ( a j - k ) j , k = 0 on some weighted sequence space l p ( + , w ) . We assume that w satisfies the Muckenhoupt A p condition and that a is a piecewise continuous function subject to some natural multiplier condition. The last condition is in particular satisfied if a is of bounded variation. Our main result is a Fredholm criterion and an index formula for T(a). It implies that the essential spectrum...

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