Complex powers of the Schrödinger operator with a homogeneous, degenerate potential
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 61-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A meromorphic extension to the entire complex plane of the Schrödinger operator with a smooth, degenerate potential homogeneous at infinity is constructed.
@article{SM_1993_75_1_a3,
     author = {A. I. Karol'},
     title = {Complex powers of the {Schr\"odinger} operator with a~homogeneous, degenerate potential},
     journal = {Sbornik. Mathematics},
     pages = {61--83},
     year = {1993},
     volume = {75},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_75_1_a3/}
}
TY  - JOUR
AU  - A. I. Karol'
TI  - Complex powers of the Schrödinger operator with a homogeneous, degenerate potential
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 61
EP  - 83
VL  - 75
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1993_75_1_a3/
LA  - en
ID  - SM_1993_75_1_a3
ER  - 
%0 Journal Article
%A A. I. Karol'
%T Complex powers of the Schrödinger operator with a homogeneous, degenerate potential
%J Sbornik. Mathematics
%D 1993
%P 61-83
%V 75
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1993_75_1_a3/
%G en
%F SM_1993_75_1_a3
A. I. Karol'. Complex powers of the Schrödinger operator with a homogeneous, degenerate potential. Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 61-83. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a3/

[1] Karol A. I., “Dzeta-funktsiya vyrozhdayuschegosya ellipticheskogo operatora”, Matem. sb., 124(166) (1984), 217–237 | MR

[2] Karol A. I., “Psevdodifferentsialnye operatory s operatornoznachnymi simvolami”, Teoriya operatorov i teoriya funktsii, no. 1, Izd-vo LGU, L., 1983, 33–46 | MR

[3] Karol A. I., “Kompleksnye stepeni operatora Shredingera s regulyarno rastuschim potentsialom”, Problemy matem. analiza, no. 11, Izd-vo LGU, L., 1990, 176–187 | MR

[4] Levendorskii S. Z., “Neklassicheskie spektralnye asimptotiki”, UMN, 1988, no. 1, 123–157 | MR | Zbl

[5] Rozenblyum G. V., Solomyak M. Z., Shubin M. A., Spektralnaya teoriya differentsialnykh operatorov, Sovr. probl. matem. fundam. napravleniya. Itogi nauki i tekhniki, 64, VINITI, M., 1989 | MR

[6] Solomyak M. Z., “Ob asimptotike spektra operatora Shrëdingera s neregulyarnym odnorodnym potentsialom”, DAN SSSR, 278:2 (1984), 291–295 | MR | Zbl

[7] Solomyak M. Z., “Asimptotika spektra operatora Shrëdingera s neregulyarnym odnorodnym potentsialom”, Matem. sb., 127(169) (1985), 21–39 | MR | Zbl

[8] Shubin M. A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978 | MR

[9] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 3. Psevdodifferentsialnye operatory, Mir, M., 1987 | MR

[10] Agmon S., “On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems”, Comm. Pure and Appl. Math., 18:4 (1965), 627–663 | DOI | MR | Zbl

[11] Aramaki J., “Complex powers of vector valued operators and their application to asymptotic behavior of eigenvalues”, J. Funct. Anal., 87:2 (1989), 294–320 | DOI | MR | Zbl

[12] Beals R., “A general calculus of pseudo-differential operators”, Duke Math. J., 42 (1975), 1–42 | DOI | MR | Zbl

[13] Fefferman C. L., “The uncertainty principle”, Bull. Amer. Math. Soc., 9:2 (1983), 129–206 | DOI | MR | Zbl

[14] Robert D., “Proprietes spectral d'operateurs pseudodifferential”, Comm. Part. Diff. Equat., 3:9 (1978), 755–826 | DOI | MR | Zbl

[15] Robert D., “Comportement asymptotique des valeurs propres d'operateurs du type Schrodinger a potential “degeners””, J. Math. pures et appl., 61:9 (1982), 275–300 | MR | Zbl

[16] Seeley R., “Complex powers of an elliptic operator”, Amer. Math. Soc. Proc. Symp. Pure Math., 10 (1968), 288–307 | MR