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Bounded $\mathbf{H_\infty}$-Calculus for Differential Operators on Conic Manifolds with Boundary

S. Coriasco·E. Schrohe·J. Seiler
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Abstract

We derive conditions that ensure the existence of a bounded $H_\infty$-calculus in weighted $L_p$-Sobolev spaces for closed extensions $\underline{A}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to differential boundary conditions $T$. In general, these conditions ask for a particular pseudodifferential structure of the resolvent $(λ-\underline{A}_T)^{-1}$ in a sector $Λ\subset\mathbf{C}$. In case of the minimal extension they reduce to parameter-ellipticity of the boundary value problem $(A,T)$. Examples concern the Dirichlet and Neumann Laplacians.

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S. Coriasco, E. Schrohe, J. Seiler. 2005-07-04. Bounded $\mathbf{H_\infty}$-Calculus for Differential Operators on Conic Manifolds with Boundary. https://doi.org/10.1080/03605300600910290

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