Extension theory for symmetric operators and boundary value problems for differential equations

On the class of extremal extensions of a nonnegative operator

“…[5], [13], [14], [15], [20], [27]. A triplet II = {H, r o, rd of a Hilbert space H with dim H = n±(A) and two linear mappings r j , j = 0,1, from dom A * into H is said to be a boundary triplet for A *, if the mapping r = (ro, rd: J -> {roJ, rd} from domA* onto H ffi H is surjective, and the abstract Green's identity…”

“…A construction of the KreIn-von Neumann and the Friedrichs extensions via such factorizations has been earlier given by V. Prokaj, Z. Sebestyen and J. Stochel [30], [32]. By a systematic use of semibounded sesquilin- The translation of these facts by means of the theory of abstract boundary value spaces (boundary pairs and boundary triplets), see [5], [13], [14], [15], [20], [27], gives a description of the class E(A) by means of abstract boundary conditions involving orthogonal projections in the parameter space, cf. [5].…”

Extensions, Dilations and Functional Models of Infinite Jacobi Matrix

“…The first result of this type belongs to Rofe-Beketov [14]. Independently, in [5] and [9], the notion of a 'space of boundary values' was introduced and all maximal dissipative, accretive, selfadjoint, and other extensions of symmetric operators were described (see [8] and also in the survey article [7]). …”

Lim-3 Durumundaki 4. Mertebe Operatörlerin Dissipatif Genişlemeleri

“…They described all maximal dissipative, acretive, self adjoint extensions of symmetric operators. For a more comprehensive discussion of extension theory of symmetric operators, the reader is referred to [6].…”