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arXiv · 1707.00923

Holomorphic families of forms, operators and $C_0$-semigroups

Hendrik Vogt·Jürgen Voigt
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Abstract

If $z\mapsto a_z$ is a holomorphic function with values in the sectorial forms in a Hilbert space, then the associated operator valued function $z\mapsto A_z$ is resolvent holomorphic. We give a proof of this result of Kato, on the basis of the Lax-Milgram lemma. We also show that the $C_0$-semigroups $T_z$ generated by $-A_z$ depend holomorphically on $z$.

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Hendrik Vogt, Jürgen Voigt. 2017-07-04. Holomorphic families of forms, operators and $C_0$-semigroups. https://doi.org/10.1007/s00605-017-1132-0

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