Reddy, Satish C. Pseudospectra of Wiener-Hopf integral operators and constant-coefficient differential operators. (English) Zbl 0805.47023 J. Integral Equations Appl. 5, No. 3, 369-403 (1993). 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. Cited in 6 Documents MSC: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47A10 Spectrum, resolvent 47E05 General theory of ordinary differential operators Keywords:\(\varepsilon\)-pseudospectrum; Volterra Wiener-Hopf integral operators; constant-coefficient differential operators with boundary conditions at one endpoint; Toeplitz matrices × Cite Format Result Cite Review PDF Full Text: DOI References: [1] P.M. Anselone and I.H. Sloan, Spectral approximations for Wiener-Hopf operators , J. Integral Equations Appl. 2 (1990), 237-261. · Zbl 0769.45001 · doi:10.1216/jiea/1181075710 [2] N.S. Bakhvalov, Numerical methods , Mir Publishers, Moscow, 1977. [3] G. Baxter, A norm inequality for a finite-section Wiener-Hopf equation , Illinois J. Math. 7 (1963), 97-103. · Zbl 0113.09101 [4] S.K. Godunov and V.S. Ryabenkii, Theory of difference schemes , North-Holland, Amsterdam, 1964. · Zbl 0116.33102 [5] I.C. Gohberg and I.A. Fel’dman, Convolution equations and projection methods for their solution , Amer. Math. Soc., Providence, RI, 1974. · Zbl 0278.45008 [6] G.H. Golub and C.F. Van Loan, Matrix computations , 2nd ed., Johns Hopkins University Press, Baltimore, 1989. · Zbl 0733.65016 [7] H. Hochstadt, Integral equations , Wiley, New York, 1973. · Zbl 0259.45001 [8] M. Kac, W.L. Murdock and G. Szegö, On the eigenvalues of certain Hermitian forms , J. Rat. Mech. Anal. 2 (1953), 767-800. · Zbl 0051.30302 [9] T. Kato, Perturbation theory for linear operators , Springer, New York, 1976. · Zbl 0342.47009 [10] M.G. Krein, Integral equations on a half-line with kernel depending on the difference of the arguments , Amer. Math. Soc. Transl. 22 (1963), 163-288. · Zbl 0119.09601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.