Let be the symmetric operator given by the restriction of to , where is a self-adjoint operator on the Hilbert space and is a linear dense set which is closed with respect to the graph norm on , the operator domain of . We show that any self-adjoint extension of such that can be additively decomposed by the sum , where both the operators and take values in the strong dual of . The operator is the closed extension of to the whole whereas is explicitly written in terms of a (abstract) boundary condition depending on and on the extension parameter , a self-adjoint operator on an auxiliary Hilbert space isomorphic (as a set) to the deficiency spaces of . The explicit connection with both Kreĭn’s resolvent formula and von Neumann’s theory of self-adjoint extensions is given.
@article{ASNSP_2003_5_2_1_1_0, author = {Posilicano, Andrea}, title = {Self-adjoint extensions by additive perturbations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {1--20}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {1}, year = {2003}, mrnumber = {1990972}, zbl = {1096.47505}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_1_0/} }
TY - JOUR AU - Posilicano, Andrea TI - Self-adjoint extensions by additive perturbations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 1 EP - 20 VL - 2 IS - 1 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_1_1_0/ LA - en ID - ASNSP_2003_5_2_1_1_0 ER -
Posilicano, Andrea. Self-adjoint extensions by additive perturbations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, pp. 1-20. http://www.numdam.org/item/ASNSP_2003_5_2_1_1_0/
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