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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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References:
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