Geodesic
Reconstruction of the Schrödinger operator with a singular potential on half-line by its prescribed essential spectrum
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 57-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Singular Schrodinger operators on $L^2([0,+\infty))$ with the potential of the form $\sum_{k=1}^{+\infty}a_k\delta_{x_k}$, where $x_k~{>}~0$ and $a_k~{\in}~\mathbb{R}$, are considered. It is constructively proved that every closed semibounded set $S\subset\mathbb{R}$ can be the essential spectrum of such operator. 
@article{VMUMM_2023_4_a9,
     author = {G. A. Agafonkin},
     title = {Reconstruction of the {Schr\"odinger} operator with a singular potential on half-line by its prescribed essential spectrum},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {57--60},
     year = {2023},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a9/}
}
TY  - JOUR
AU  - G. A. Agafonkin
TI  - Reconstruction of the Schrödinger operator with a singular potential on half-line by its prescribed essential spectrum
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 57
EP  - 60
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a9/
LA  - ru
ID  - VMUMM_2023_4_a9
ER  - 
%0 Journal Article
%A G. A. Agafonkin
%T Reconstruction of the Schrödinger operator with a singular potential on half-line by its prescribed essential spectrum
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 57-60
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a9/
%G ru
%F VMUMM_2023_4_a9
G. A. Agafonkin. Reconstruction of the Schrödinger operator with a singular potential on half-line by its prescribed essential spectrum. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 57-60. http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a9/

[1] Mirzoev K.A., “Operatory Shturma–Liuvillya”, Tr. Mosk. matem. o-va, 75, no. 2, 2014, 335–359 | Zbl

[2] Kostenko A.S., Malamud M.M., “1-D Schrodinger operators with local point interactions on a discrete set”, J. Diff. Equat, 249:2 (2010), 253–304 | DOI | MR | Zbl

[3] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[4] Savchuk A.M., Shkalikov A.A., “Operatory Shturma–Liuvillya s potentsialami-raspredeleniyami”, Tr. Mosk. matem. o-va, 64, 2003, 159–212 | Zbl

[5] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 4, Analiz operatorov, Mir, M., 1982 | MR