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arXiv · 1706.08314

On the construction and convergence of traces of forms

Hichem BelHadjAli·Ali BenAmor·Christian Seifert·Amina Thabet
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Abstract

We elaborate a new method for constructing traces of quadratic forms in the framework of Hilbert and Dirichlet spaces. Our method relies on monotone convergence of quadratic forms and the canonical decomposition into regular and singular part. We give various situations where the trace can be described more explicitly and compute it for some illustrating examples. We then show that Mosco convergence of Dirichlet forms implies Mosco convergence of a subsequence of their approximating traces and that asymptotic compactness of Dirichlet forms yields asymptotic compactness of their traces.

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Hichem BelHadjAli, Ali BenAmor, Christian Seifert, Amina Thabet. 2017-06-26. On the construction and convergence of traces of forms. https://arxiv.org/abs/1706.08314

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