Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

Böttcher, A.; Seybold, M.

Studia Mathematica, Tome 141 (2000), p. 121-144 / Harvested from The Polish Digital Mathematics Library

Résumé

The discrete Wiener-Hopf operator generated by a function $a (e^{i θ})$ with the Fourier series $\sum_{n \in ℤ} a_{n} e^{i n θ}$ is the operator T(a) induced by the Toeplitz matrix ${(a_{j - k})}_{j, k = 0}^{\infty}$ 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.

Publié le : 2000-01-01

Zbl 0971.47021

EUDML-ID : urn:eudml:doc:216812

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     author = {A. B\"ottcher and M. Seybold},
     title = {Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {121-144},
     zbl = {0971.47021},
     language = {en},
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Böttcher, A.; Seybold, M. Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight. Studia Mathematica, Tome 141 (2000) pp. 121-144. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv143i2p121bwm/

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