Q-functions and boundary triplets of nonnegative operators

2013/09/26 by Yury Arlinskii, Arlinskii, Yury, Seppo Hassi +1
Mathematics · #47A56 #47B25 #47B65 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A56 #msc:47B25 #msc:47B65

paper · pdf · doi:10.48550/arxiv.1309.6882

arxiv created 2013/09/26 · arxiv updated 2013/09/27

Abstract

Operator-valued Q-functions for special pairs of nonnegative selfadjoint extensions of nonnegative not necessarily densely defined operators are defined and their analytical properties are studied. It is shown that the Kre\uın-Ovcharenko statement announced in \citeKrO2 is valid only for Q-functions of densely defined symmetric operators with finite deficiency indices. A general class of boundary triplets for a densely defined nonnegative operator is constructed such that the corresponding Weyl functions are of Kre\uın-Ovcharenko type.

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