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Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

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Böttcher A., Seybold M.

Studia Mathematica

2000

tom 143

nr 2

121-144

The discrete Wiener-Hopf operator generated by a function $a(e^{iθ})$ with the Fourier series $∑_{n∈ℤ} a_n e^{inθ}$ is the operator T(a) induced by the Toeplitz matrix $(a_{j-k})_{j,k = 0}^∞$ on some weighted sequence space $l^p(ℤ_{+}, w)$. 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 of T(a) results from the essential range of a by filling in certain horns between the endpoints of each jump. The shape of these horns is determined by the indices of powerlikeness of the weight w.

Ograniczanie wyników

1 Studia Mathematica

1 Böttcher A.

1 Seybold M.

1 2000

Wyniki wyszukiwania

Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight