Geodesic
The Negative Spectrum of a Class of Two-Dimensional Schrödinger Operators with Potentials Depending Only on Radius
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 85-87 
A. Laptev. The Negative Spectrum of a Class of Two-Dimensional Schrödinger Operators with Potentials Depending Only on Radius. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 85-87. http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a9/
@article{FAA_2000_34_4_a9,
     author = {A. Laptev},
     title = {The {Negative} {Spectrum} of a {Class} of {Two-Dimensional} {Schr\"odinger} {Operators} with {Potentials} {Depending} {Only} on {Radius}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {85--87},
     year = {2000},
     volume = {34},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a9/}
}
TY  - JOUR
AU  - A. Laptev
TI  - The Negative Spectrum of a Class of Two-Dimensional Schrödinger Operators with Potentials Depending Only on Radius
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2000
SP  - 85
EP  - 87
VL  - 34
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a9/
LA  - ru
ID  - FAA_2000_34_4_a9
ER  - 
%0 Journal Article
%A A. Laptev
%T The Negative Spectrum of a Class of Two-Dimensional Schrödinger Operators with Potentials Depending Only on Radius
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2000
%P 85-87
%V 34
%N 4
%U http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a9/
%G ru
%F FAA_2000_34_4_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

[1] Birman M. Sh., Matem. sb., 55 (1961), 125–174 | MR | Zbl

[2] Birman M. Sh., Laptev A., “The negative discrete spectrum of a two-dimensional Schrödinger operator”, Comm. Pure Appl. Math., 49 (1996), 967–997 | 3.0.CO;2-5 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[3] Birman M. Sh., Solomyak M. Z., “Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations”, Estimates and asymptotics for discrete spectra of integral and differential equations, Adv. Soviet Math., 7, Amer. Math. Soc., Providence, RI, 1991, 1–55 | MR

[4] Cwikel M., “Weak type estimates for singular values and the number of bound states of Schrödinger operators”, Ann. Math., 106 (1977), 93–100 | DOI | MR | Zbl

[5] Hundertmark D., Laptev A., Weidl T., “New bounds on the Lieb-Thirring constants”, Invent. Math., 140 (2000), 693–704 | DOI | MR | Zbl

[6] Hundertmark D., Lieb E. H., Thomas L. E., “A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator”, Adv. Theor. Math. Phys., 2 (1998), 719–731 | DOI | MR | Zbl

[7] Laptev A., Netrusov Yu., Amer. Math. Soc. Transl. Ser. 2, 189, 1998, 178–186

[8] Lieb E. H., “Bounds on the eigenvalues of the Laplace and Schrödinger operators”, Bull. Amer. Math. Soc., 82 (1976), 751–753 | DOI | MR | Zbl

[9] Maz'ya V., Sobolev Spaces, Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1985 | MR

[10] Opic B., Kufner A., Hardy-Type Inequalities, Pitman Research Notes in Mathematics Series, 219, Longman Scientific Technical, Harlow, 1990 | MR | Zbl

[11] Rozenblyum G. V., Izv. VUZov, ser. matem., 1976, no. 1, 75–86 | MR | Zbl

[12] Schwinger J., “On the bound states of a given potential”, Proc. Nat. Acad. Sci., 47 (1961), 122–129 | DOI | MR

[13] Solomyak M., Israel J. Math., 86 (1994), 253–276 | DOI | MR

[14] Solomyak M., “Spectral problems related to the critical exponent in the Sobolev embedding theorem”, Proc. London Math. Soc., 71 (1995), 53–75 | DOI | MR | Zbl

[15] Weidl T., “On the Lieb-Thirring constants $L_{\gamma,1}$ for $\gamma\geq 1/2$”, Comm. Math. Phys., 178 (1996), 135–146 | DOI | MR | Zbl