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Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators

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Gnewuch M.

Colloquium Mathematicum

2006

tom 105

nr 1

105-125

We consider a special class of sums of non-commuting positive operators on L²-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 ≤ p ≤ ∞. 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.

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1 Colloquium Mathematicum

1 Gnewuch M.

1 2006

Wyniki wyszukiwania

Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators