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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Transmission Eigenvalues and Upper Triangular Comp
actness - Sylvester\, J (University of Washington)
DTSTART;TZID=Europe/London:20110802T111500
DTEND;TZID=Europe/London:20110802T120000
UID:TALK32204AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32204
DESCRIPTION:The interior transmission eigenvalue problem can b
e formulated as a 2x2 system of pdes\, where one o
f the two unknown functions must satisfy too many
boundary conditions\, and the other too few. The s
ystem is not self-adjoint and the resolvent is not
compact. \n\nUnder the hypothesis that the contra
st satisfies a coercivity condition on the boundar
y of the domain\, we show that the corresponding o
perator has Upper Triangular Compact Resolvent and
that the analytic Fredholm theorem holds for such
opertors. \n\nAs corollaries\, we can show that t
he set of (complex) interior transmission eigenval
ues is a (possibly empty) discrete set which depen
ds contunuously on the contrast\, and that eigenfu
nctions must be linearly independent. This is diff
erent from previous results because the contrast n
eed not have a constant sign (or be real valued) i
n the interior of the domain. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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