On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactionsReport as inadecuate



 On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions


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By Birman and Skvortsov it is known that if $\Omegasf$ is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain $H^2\Omegasf\cap H^1 0\Omegasf$ is a closed symmetric operator with deficiency indices $n,n$. Here we provide a Kre\u\i n-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on $\Omegasf$, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions.



Author: Andrea Posilicano

Source: https://archive.org/







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