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.
[1] Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analytic.
The full statement of the conjecture as given by Auscher et al. is: "the domain of the square root of a uniformly complex elliptic operator
[2] The problem remained unresolved for nearly a half-century, until in 2001 it was jointly solved in the affirmative by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Philippe Tchamitchian.