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Pseudospectra of Wiener-Hopf integral operators and constant-coefficient differential operators. (English) Zbl 0805.47023
Summary: A number \(z\in \mathbb{C}\) is in the \(\varepsilon\)-pseudospectrum of a linear operator \(A\) if \(\| (zI- A)^{-1}\|\geq \varepsilon^{-1}\). In this paper, we investigate the \(\varepsilon\)-pseudospectra of Volterra Wiener-Hopf integral operators and constant-coefficient differential operators with boundary conditions at one endpoint for the interval \([0,b]\). We show that although the spectra of these operators are not continuous in the limit \(b\to \infty\), the \(\varepsilon\)-pseudospectra are continuous as \(b\to\infty\) for all \(\varepsilon>0\). These results are an extension of previous work on the pseudospectra of Toeplitz matrices.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A10 Spectrum, resolvent
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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