On the approximation numbers of large Toeplitz matrices.
The discrete Wiener-Hopf operator generated by a function with the Fourier series is the operator T(a) induced by the Toeplitz matrix on some weighted sequence space . We assume that w satisfies the Muckenhoupt 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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