Kato's conjecture

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Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of University of California at Berkeley. Kato initially posed the problem in 1953.

In its most simplistic form, the problem deals with the theory of waves moving through various mediums. In a bit more detail, Kato asked whether the square root of certain elliptic operators, defined via functional calculus, is analytic.

The problem had plagued mathematicians for nearly a half-century, until it was jointly solved in 2001 by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Philippe Tchamitchian. The solution was published in 2002 in the Annals of Mathematics journal.

[edit] References

Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh and Philippe Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on Rⁿ. Annals of Mathematics, volume 156, number 2, pages 633–654, 2002.