To the theory of nonnegative point Hamiltonians on a plane and in the space
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605524920 | ||
| 003 | CHVBK | ||
| 005 | 20210128100756.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10958-014-2204-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-014-2204-5 | ||
| 100 | 1 | |a Kovalev |D Yurii |u V. Dal' East-Ukrainian National University, 20a, Molodezhnyi Block, 91034, Lugansk, Ukraine |4 aut | |
| 245 | 1 | 0 | |a To the theory of nonnegative point Hamiltonians on a plane and in the space |h [Elektronische Daten] |c [Yurii Kovalev] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2014 | ||
| 690 | 7 | |a Point interactions |2 nationallicence | |
| 690 | 7 | |a Riesz basis |2 nationallicence | |
| 690 | 7 | |a Friedrichs extension |2 nationallicence | |
| 690 | 7 | |a Krein extension |2 nationallicence | |
| 690 | 7 | |a transversality |2 nationallicence | |
| 690 | 7 | |a disjointness |2 nationallicence | |
| 690 | 7 | |a boundary triplets |2 nationallicence | |
| 690 | 7 | |a Weyl function |2 nationallicence | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 204/3(2015-01-01), 315-332 |x 1072-3374 |q 204:3<315 |1 2015 |2 204 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-014-2204-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-014-2204-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Kovalev |D Yurii |u V. Dal' East-Ukrainian National University, 20a, Molodezhnyi Block, 91034, Lugansk, Ukraine |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 204/3(2015-01-01), 315-332 |x 1072-3374 |q 204:3<315 |1 2015 |2 204 |o 10958 | ||