In this paper, we investigate the ε-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 → ∞, the εpseudospectra are continuous as b → ∞ for all ε > 0. These results are an extension of previous work on the pseudospectra of Toeplitz matrices.
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A 1993 study studied this question.