Kato's conjecture

Kato's conjecture

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

Kato asked whether the square root of certain elliptic operators, defined via functional calculus, are 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.

References

* Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh and Philippe Tchamitchian, [http://www.math.princeton.edu/~annals/issues/2002/Auscher.pdf 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.

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