# Functional Calculus via the extension technique: a first hitting time approach

@inproceedings{Hauer2021FunctionalCV, title={Functional Calculus via the extension technique: a first hitting time approach}, author={Daniel Hauer and David Lee}, year={2021} }

In this article, we present a solution to the problem: Which type of linear operators can be realized by the Dirichlet-to-Neumann operator associated with the operator −∆ − a(z) ∂ 2 ∂z on an extension problem? which was raised in the pioneering work [Comm. Par.Diff. Equ. 32 (2007)] by Caffarelli and Silvestre. In fact, we even go a step further by replacing the negative Laplace operator −∆ on R by an m-accretive operator A on a general Banach space X and the Dirichlet-to-Neumann operator by the…

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