In this article, we study questions of uniqueness of form extension for certain magnetic Schrodinger forms. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. We review this concept in an abstract setting and give a characterization in terms of the associated forms. Then we use it to prove a theorem that transfers uniqueness of form extension of a dominating form to that of a dominated form. This result is applied in two concrete situations: magnetic Schrodinger forms on graphs and on domains in Euclidean space.

中文翻译：

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形式扩展的唯一性和半群的支配

在本文中，我们研究了某些磁性薛定谔形式的形式扩展的唯一性问题。该方法基于有序希尔伯特空间理论和半群支配的概念。我们在一个抽象的环境中回顾这个概念，并根据相关的形式给出一个特征。然后我们用它来证明一个定理，将支配形式的形式外延的唯一性转移到支配形式的形式扩展的唯一性。该结果适用于两种具体情况：图上的磁薛定谔形式和欧几里得空间中的域。