PSEUDOSPECTRA OF WIENER-HOPF INTEGRAL OPERATORS AND CONSTANT-COEFFICIENT DIFFERENTIAL OPERATORS

A number z ∈ C is in the ε-pseudospectrum of a linear operator A if ∥(zI − A)−1∥ ≥ ε−1. 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 ε-pseudospectra are continuous as b → ∞ for all ε > 0. These results are an extension of previous work on the pseudospectra of Toeplitz matrices.