2019/10/23 by Seppo Hassi, Hassi, Seppo, Jean-Philippe Labrousse +3
Computer Science · Engineering · #47B25 #47B65 #Advanced Algebra and Logic #Constraint Satisfaction and Optimization #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A06 #Scheduling and Optimization Algorithms #Secondary 47A12
paper · pdf · doi:10.48550/arxiv.1910.10645
openalex publication_date 2019/10/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The selfadjoint extensions of a closed linear relation R from a Hilbert\nspace mathfrak H1 to a Hilbert space mathfrak H2 are considered in\nthe Hilbert space mathfrak H1\⊕ mathfrak H2 that contains the\ngraph of R. They will be described by 2 \× 2 blocks of linear relations\nand by means of boundary triplets associated with a closed symmetric relation\nS in mathfrak H1 \⊕ mathfrak H2 that is induced by R. Such a\nrelation is characterized by the orthogonality property rm dom , S \⊥\n rm ran , S and it is nonnegative. All nonnegative selfadjoint extensions\nA, in particular the Friedrichs and Kre u in-von Neumann extensions, are\nparametrized via an explicit block formula. In particular, it is shown that A\nbelongs to the class of extremal extensions of S if and only if rm dom ,\nA \⊥ rm ran , A. In addition, using asymptotic properties of an\nassociated Weyl function, it is shown that there is a natural correspondence\nbetween semibounded selfadjoint extensions of S and semibounded parameters\ndescribing them if and only if the operator part of R is bounded.\n