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Differentiable $L^p$-functional calculus for certain sums of non-commuting operators
We consider a special class of sums of non-commuting positive operators on $L^2$-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable $L^p$-functional calculus for $1\leq p \leq \infty$. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.