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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Recent progress in the spectral theory of first or
der elliptic systems - Vassiliev\, D (University C
ollege London)
DTSTART;TZID=Europe/London:20120918T101000
DTEND;TZID=Europe/London:20120918T105000
UID:TALK39846AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39846
DESCRIPTION:The talk deals with the distribution of eigenvalue
s of a linear self-adjoint elliptic operator. The
eigenvalue problem is considered in the determinis
tic setting\, i.e. the coefficients of the operato
r are prescribed smooth functions. The objective
is to derive a two-term asymptotic formula for the
counting function (number of eigenvalues between
zero and a positive lambda) as lambda tends to plu
s infinity.\n\nThere is an extensive literature on
the subject (see\, for example\, [1])\, mostly de
aling with scalar operators. It has always been ta
ken for granted that all results extend in a strai
ghtforward manner to systems. However\, the author
has recently discovered [2\,3] that all previous
publications on first order systems give formulae
for the second asymptotic coefficient that are eit
her incorrect or incomplete (i.e. an algorithm for
the calculation of the second asymptotic coeffici
ent rather than an explicit formula). The aim of t
he talk is to explain the spectral theoretic diffe
rence between scalar operators and systems and to
present the correct formula for the second asympto
tic coefficient.\n\n[1] Yu.Safarov and D.Vassiliev
\, The asymptotic distribution of eigenvalues of p
artial differential operators\, American Mathemati
cal Society\, 1997 (hardcover)\,\n1998 (softcover)
.\n\n[2] Preprint arXiv:1204.6567.\n\n[3] Preprint
arXiv:1208.6015.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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