M. Kreĭn’s Research on Semi-Bounded Operators, its Contemporary Developments, and Applications

The Krein–von Neumann extension and its connection to an abstract buckling problem

“…Concluding this section, we point out that a great variety of additional results for the Krein-von Neumann extension can be found in the very extensive list of references in [8], [9], and [26].…”

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

“…In the case of a nondensely defined nonnegative symmetric operator A, characterizations of its Friedrichs extension A F and its Kreȋn extension A K can be found in [7,26], a description of its generalized resolvents of the class C .A/ was given in [35]. For descriptions of maximal accretive and maximal sectorial extensions of sectorial and, in particular, nonnegative operators see surviews [8][9][10] and references therein.…”

The nonproper dissipative extensions of a dual pair

“…Thus, the theory of dissipative extensions of a given operator is an extensively studied problem (for an overview, we recommend the surveys [5,9] and all the references therein). Besides the classical results of von Neumann on the theory of selfadjoint extensions of a given symmetric operator [36] and of Kreȋn, Birman, Vishik and Grubb on positive selfadjoint and maximally sectorial extensions of a given symmetric operator with positive numerical range [29,41,11,26,1,2], let us also mention the results of authors like Arlinskiȋ, Belyi, Derkach, Kovalev, Malamud, Mogilevskii and Tsekanovskiȋ [4,6,7,8,17,18,33,34,35,39,40] who have made many contributions using form methods and boundary triples in order to determine maximally sectorial and maximally accretive extensions of a given sectorial operator.…”