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arXiv · 2308.06400

The Krein transform and semi-bounded extensions of semi-bounded linear relations

Josué I. Rios-Cangas
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Abstract

The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an involution for linear relations. On the other hand, a semi-bounded linear relation has closed semi-bounded symmetric extensions with semi-bounded selfadjoint extensions. A self-consistent theory of semi-bounded symmetric extensions of semi-bounded linear relations is presented. By using The Krein transform, a formula of positive extensions of quasi-null relations is provided.

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Josué I. Rios-Cangas. 2023-08-11. The Krein transform and semi-bounded extensions of semi-bounded linear relations. https://arxiv.org/abs/2308.06400

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