Pseudospectra of linear operators. (English) Zbl 0896.15006

Trefethen, Lloyd N.

SIAM Rev. 39, No. 3, 383-406 (1997).

This overview is a companion to the author’s article [Pitman Res. Notes Math. Ser. 260, 234-266 (1992; Zbl 0798.15005)], where the matrix case was treated.
In this paper newer results on the pseudospectrum of operators are presented and thoroughly discussed. It contains ten examples for pseudospectra of bounded and unbounded operators, e.g. the Wiener-Hopf operator, plane Poiseuille flow operator, Orr-Sommerfeld operator, a differentiation operator.

Reviewer: L.Elsner (Bielefeld)

MSC:

15A18	Eigenvalues, singular values, and eigenvectors
76E05	Parallel shear flows in hydrodynamic stability
47A10	Spectrum, resolvent
65F15	Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

resolvent; nonnormality; pseudospectrum; Wiener-Hopf operator; plane Poiseuille flow operator; Orr-Sommerfeld operator; differentiation operator

Citations:

Zbl 0798.15005