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.[1]

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

The problem remained unresolved for nearly a half-century, until it was jointly solved in 2001 by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Philippe Tchamitchian.[2]

References

  1. ↑ Kato, Tosio (1953). "Integration of the equation of evolution in a Banach space". J. Math. Soc. Japan 5: 208–234. doi:10.2969/jmsj/00520208. MR 0058861.
  2. ↑ Auscher, Pascal; Hofmann, Steve; Lacey, Michael; McIntosh, Alan; Tchamitchian, Philippe (2002). "The solution of the Kato square root problem for second order elliptic operators on Rn". Annals of Mathematics 156 (2): 633–654. doi:10.2307/3597201. MR 1933726.
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