Still more proof that I was and am not smart enough to work in pure math!
:-)
http://hosted.ap.org/dynamic/stories/M/MATH_PROBLEM?SITE=FLTAM&SECTION=UShttp://www.kcstar.com/http://cnn.netscape.cnn.com/story.jsp?id=2005122704220001702241&dt=20051227042200&w=APO&coview=Dec 27, 7:22 PM EST
Prof Honored for Solving Old Math Problem
KANSAS CITY, Mo. (AP) -- A professor at the University of Missouri-Columbia is being recognized for solving a math problem that had stumped his peers for more than 40 years.
The achievement has landed Steven Hofmann an invitation to speak next spring at the 2006 International Congress of Mathematicians in Madrid, Spain.<snip>
The problem, known as Kato's Conjecture, applies to the theory of waves moving through different media, such as seismic waves traveling through different types of rock. It bears the name of Tosio Kato, a now-deceased mathematician at the University of California-Berkeley, who posed the problem in research papers first written in 1953 and again in 1961.
Part of the problem, called the one-dimensional version, was solved about 20 years ago. Though it was a breakthrough, work remained. Hofmann solved the problem in all its dimensions in a 120-word paper that he wrote with several colleagues - Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh and Philippe Tchamitchian.<snip>
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harmonic analysis
http://www.math.sciences.univ-nantes.fr/edpa/2001/pdf/tchami.pdfhttp://archive.numdam.org/article/JEDP_2001____A14_0.pdf Kato's conjecture, stating that the domain of the square root of any accretive operator $L=-\dive(A\nabla)$ with bounded measurable coefficients in $\mathbb{R}^n$ is the Sobolev space $H^1(\mathbb{R}^n)$, i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, M\texsuperscript^{c}Intosh and the author. These notes present the result and explain the strategy of proof.