Pseudospectra of semiclassical (pseudo) differential operators
(2004) In Communications on Pure and Applied Mathematics 57(3). p.384415 Abstract
 The pseudospectra (or spectral instability) of nonselfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.
The explanation is that for nonnormal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasimodes, i.e., approximate local solutions
to the eigenvalue problem. The quasimodes appear since the NirenbergTreves condition (Psi)... (More)  The pseudospectra (or spectral instability) of nonselfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.
The explanation is that for nonnormal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasimodes, i.e., approximate local solutions
to the eigenvalue problem. The quasimodes appear since the NirenbergTreves condition (Psi) is not satisfied for topological reasons. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/289796
 author
 Dencker, Nils ^{LU} ; Sjostrand, J and Zworski, M
 organization
 publishing date
 2004
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 principal type, nonselfadjoint operators, semiclassical operators, pseudospectrum
 in
 Communications on Pure and Applied Mathematics
 volume
 57
 issue
 3
 pages
 384  415
 publisher
 John Wiley & Sons
 external identifiers

 wos:000188201100004
 scopus:1842832252
 ISSN
 00103640
 DOI
 10.1002/cpa.20004
 language
 English
 LU publication?
 yes
 id
 07a0b55a4c444f4c887970a525148f2e (old id 289796)
 date added to LUP
 20071023 11:01:39
 date last changed
 20171022 04:35:01
@article{07a0b55a4c444f4c887970a525148f2e, abstract = {The pseudospectra (or spectral instability) of nonselfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.<br/><br> <br/><br> The explanation is that for nonnormal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasimodes, i.e., approximate local solutions<br/><br> to the eigenvalue problem. The quasimodes appear since the NirenbergTreves condition (Psi) is not satisfied for topological reasons.}, author = {Dencker, Nils and Sjostrand, J and Zworski, M}, issn = {00103640}, keyword = {principal type,nonselfadjoint operators,semiclassical operators,pseudospectrum}, language = {eng}, number = {3}, pages = {384415}, publisher = {John Wiley & Sons}, series = {Communications on Pure and Applied Mathematics}, title = {Pseudospectra of semiclassical (pseudo) differential operators}, url = {http://dx.doi.org/10.1002/cpa.20004}, volume = {57}, year = {2004}, }