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<DIV><FONT face=Arial size=2>Gentile prof./dott., la avvertiamo che nei prossimi
giorni alla Scuola Normale si terrà, nell'ambito del Colloquio De Giorgi, il
seguente seminario di matematica:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Giovedì 27 febbraio ore 15:00, Aula
Mancini</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Prof. Philippe Tchamitchian</STRONG> -
Univeristé d'Aix-Marseille III</FONT></DIV>
<DIV><FONT face=Arial size=2>"The square root problem"</FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>
Abstract</FONT></FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>This problem has been raised by Kato in the
early 60's, motivated by perturbation theory and functional calculus. It is
about the square root of differential operators under divergence form, and
consists of the following two questions:<BR>1. in the self-adjoint case, where
it is easy to check that this square root has the natural Sobolev space for
domain, how does it depend on the coefficients ?<BR>2. In the more general case
of maximal accretive operators, not necessarily self-adjoint, does the domain of
the square root still coincide with the natural Sobolev space?<BR>These two
questions have been completely answered recently, through<BR>the works of
Auscher, Hofmann, Lacey, Lewis, McIntosh and the speaker.<BR>The proofs involve
ideas from real harmonic analysis, functional calculus and the regularity theory
for partial differential operators.<BR>The talk will present how these different
aspects have to be taken<BR>into account in answering Kato's
questions.<BR></FONT></FONT><FONT><BR><FONT face=Arial size=2>Cordiali
saluti</FONT></FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>SEGRETERIA DELLA CLASSE DI
SCIENZE</FONT></DIV></FONT></BODY></HTML>