Conjetura de Kato sobre los abiertos de R.
Pascal Auscher, Philippe Tchamitchian (1992)
Revista Matemática Iberoamericana
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We prove Kato's conjecture for second order elliptic differential operators on an open set in dimension 1 with arbitrary boundary conditions. The general case reduces to studying the operator T = - d/dx a(x) d/dx on an interval, when a(x) is a bounded and accretive function. We show for the latter situation that the domain of T is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function a(x).