caa a22 4500 605524920 CHVBK 20210128100756.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10958-014-2204-5 doi (NATIONALLICENCE)springer-10.1007/s10958-014-2204-5 Kovalev Yurii V. Dal' East-Ukrainian National University, 20a, Molodezhnyi Block, 91034, Lugansk, Ukraine aut To the theory of nonnegative point Hamiltonians on a plane and in the space [Elektronische Daten] [Yurii Kovalev] Let Y be a countable set of points in ℝ d , d = 2, 3, such that d *(Y) := inf{|y − y′| : y, y′ ∈ Y, y ≠ y′} > 0. Using the connection between the Sobolev Space W 2 2 (ℝ d ) and the Hilbert space ℓ2, it is proved that the system of Dirac's delta functions {δ(x − y), y ∈ Y, x ∈ Rd, d = 2, 3} forms the Riesz basis in its linear hull in W 2 − 2 (ℝ d ). The properties of the Friedrichs and Krein extensions for a nonnegative symmetric operator A Y , d := −Δ: d o m A Y , d = f ∈ W 2 2 ℝ d : f y = 0 , y ∈ Y $$ \mathrm{d}\mathrm{o}\mathrm{m}\left({A}_{Y,d}\right)=\left\{f\in {W}_2^2\left({\mathbb{R}}^d\right):f(y)=0,\;y\in Y\right\} $$ are studied. Boundary triplets for the operators A Y,2 * and A Y,3 * are constructed in a formally unified way. Springer Science+Business Media New York, 2014 Point interactions nationallicence Riesz basis nationallicence Friedrichs extension nationallicence Krein extension nationallicence transversality nationallicence disjointness nationallicence boundary triplets nationallicence Weyl function nationallicence Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 204/3(2015-01-01), 315-332 1072-3374 204:3<315 2015 204 10958 https://doi.org/10.1007/s10958-014-2204-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-014-2204-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kovalev Yurii V. Dal' East-Ukrainian National University, 20a, Molodezhnyi Block, 91034, Lugansk, Ukraine aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 204/3(2015-01-01), 315-332 1072-3374 204:3<315 2015 204 10958