The solution by iteration of a composed K-positive definite operator equation in a Banach space.
The solution of the Kato problem in two dimensions.
We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L12(R2) → L2(R2).[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators
2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.In this paper classes of K^r -operators are considered – the classes of bounded and unbounded operators A with equal domains of A and A*, finite dimensional imaginary parts and presented as a coupling of a dissipative operator and an antidissipative one with real absolutely continuous spectra and the class of unbounded dissipative K^r -operators A with different domains of A and A* and with real absolutely continuous spectra....