New examples of pseudospectra of differential operators

Lloyd N. Trefethen
http://www.comlab.ox.ac.uk/oucl/work/nick.trefethen/

Oxford University Computing Laboratory
Wolfson Bldg., Parks Rd.
Oxford OX1 3QD, UK


Abstract

When I published the article "Pseudospectra of linear operators" in SIAM Review in 1997 built around ten examples of non-normal operators with interesting pseudospectra, these were more or less all the interesting examples I knew. Since then a broader view has emerged, thanks especially to links pointed out by E. B. Davies and M. Zworski with certain mathematical phenomena of semiclassical mechanics. These developments have highlighted the basic distinction between "boundary pseudomodes" and "wave packet pseudomodes" and opened to door to almost arbitrary behaviors of both kinds. This talk, based on joint work with Tom Wright, will present ten more examples of pseudospectra of differential and integral linear operators that have appeared since 1997.