Geodesic
Behaviour of the scattering amplitude of the Helmholtz resonator near a resonance
Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1259-1273 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Scattering by the Helmholtz resonator is considered and the behaviour of the scattering amplitude near a resonance is studied. A relation between the symmetry properties of the resonator and the symmetry properties of the scattering amplitude is established. 
@article{SM_2001_192_9_a0,
     author = {A. A. Arsen'ev},
     title = {Behaviour of the~scattering amplitude of {the~Helmholtz} resonator near a~resonance},
     journal = {Sbornik. Mathematics},
     pages = {1259--1273},
     year = {2001},
     volume = {192},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_9_a0/}
}
TY  - JOUR
AU  - A. A. Arsen'ev
TI  - Behaviour of the scattering amplitude of the Helmholtz resonator near a resonance
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1259
EP  - 1273
VL  - 192
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_9_a0/
LA  - en
ID  - SM_2001_192_9_a0
ER  - 
%0 Journal Article
%A A. A. Arsen'ev
%T Behaviour of the scattering amplitude of the Helmholtz resonator near a resonance
%J Sbornik. Mathematics
%D 2001
%P 1259-1273
%V 192
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2001_192_9_a0/
%G en
%F SM_2001_192_9_a0
A. A. Arsen'ev. Behaviour of the scattering amplitude of the Helmholtz resonator near a resonance. Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1259-1273. http://geodesic.mathdoc.fr/item/SM_2001_192_9_a0/

[1] Shenk N., Thoe D., “Eigenfunction expansions and scattering theory for perturbation of $-\Delta$”, J. Math. Anal. Appl., 36 (1971), 313–351 | DOI | MR | Zbl

[2] Shenk N., Thoe D., “Resonant states and poles of the scattering matrix for perturbation of $-\Delta$”, J. Math. Anal. Appl., 37 (1972), 467–491 | DOI | MR | Zbl

[3] Yafaev D. R., Matematicheskaya teoriya rasseyaniya, Izd-vo S.-Peterburgskogo un-ta, SPb., 1994 | MR

[4] Arsenev A. A., “Rezonansnye svoistva matritsy rasseyaniya dlya odnomernogo operatora Shredingera s lovushechnym potentsialom”, Matem. sb., 187:6 (1996), 3–20 | MR | Zbl

[5] Albeverio S., Høegh-Kron R., “Perturbations of resonances in quantum mechanics”, J. Math. Anal. Appl., 101 (1989), 491–513 | DOI | MR

[6] Hislop P. D., Martinez A., “Scattering resonances of a Helmholtz resonator”, Indiana Univ. Math. J., 40:2 (1991), 767–788 | DOI | MR | Zbl

[7] Fernandez C. A., “Resonances in scattering by a resonator”, Indiana Univ. Math. J., 34:1 (1985), 115–125 | DOI | MR | Zbl