2023/08/11 by Josué I. Rios-Cangas, Rios-Cangas, Josué I.
Engineering · Physics and Astronomy · #47B65 #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Force Microscopy Techniques and Applications #Mathematical Physics (math-ph) #Primary 47A06 #Secondary 47A45
paper · pdf · doi:10.48550/arxiv.2308.06400
openalex publication_date 2023/08/11 · openalex created_date 2023/08/16 · openalex updated_date 2026/08/01
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.