Preprint (PDF),
27 January 2013

Positivity**18** (2014), 235–256

Original version at doi:10.1007/s11117-013-0243-7

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Positivity

Original version at doi:10.1007/s11117-013-0243-7

Citations on Google Scholar

By analysing some explicit examples we investigate the positivity and non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator associated with the operator \(\Delta +\lambda I\) as \(\lambda\) varies. It is known that the semigroup is positive if \(\lambda<\lambda_1\), where \(\lambda_1\) is the principal eigenvalue of \(-\Delta\) with Dirichlet boundary conditions. We show that it is possible for the semigroup to be non-positive, eventually positive or positive and irreducible depending on \(\lambda>\lambda_1\).

**AMS Subject Classification (2000):**
47D06, 35B09, 35C10

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