Spectral Theory in Banach Spaces and Harmonic Analysis
Alan G.R. McIntosh
Australian National University, Canberra, AustraliaNigel Kalton
University of Missouri, Columbia, USALutz Weis
Universität Karlsruhe, Germany
You need to subscribe to download the article.
Abstract
The conference was motivated by the recent solutions of two longstanding questions. The first one is Kato's square root problem, i.e.~whether for an elliptic operator in divergence form on we have for . After a long development over 40 years this was shown in a joint effort by P.~Auscher, S.~Hofmann, M.~Lacey, A.~McIntosh and Ph.~Tchamitchian. For a new approach to this important result via Dirac operators and extensions of it, see the abstracts of A.~McIntosh and S.~Keith. The second problem, attributed to Br{\'e}zis in the eighties, asks whether the Cauchy problem for every generator of an analytic semigroup in an -space with $1