Geodesic
Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II. $l=1$
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 24-34 
Yu. G. Shondin. Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II. $l=1$. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 24-34. http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a2/
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     author = {Yu. G. Shondin},
     title = {Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix {II.~}$l=1$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--34},
     year = {1985},
     volume = {65},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description is given of “inequivalen” Hamiltonians on a Hilbert space $\mathfrak{H}^N$ which is obtained by restricting the Pontryagin space of the form $$ \Pi_1^N=\mathscr{H}_{+}^N[+]\mathscr{H}_{-},\quad\mathscr{H}_{+}^N=L_2(R_3)\oplus C_{N+1}\quad\mathscr{H}_{-}=C_1 $$ to a hyperplane of unit codimensionality, the Hamiltonians leading to a rational $S$ matrix in the sense of scattering theory in the pair of spaces $L_2$ and $\mathfrak{H}^N$. The use in intermediate considerations of spaces with indefinite metric is an essential and distinctive feature of the ease considered. Hamiltonians on $\mathfrak{H}^1$ are characterized as models of generalized pointlike interactions.

[1] Shondin Yu. G., TMF, 64:3 (1985), 432–441 | MR

[2] Tsirova I. S., Shirokov Yu. M., TMF, 46:3 (1981), 310–315 | MR | Zbl

[3] Shirokov Yu. M., TMF, 46:3 (1981), 291–299 | MR | Zbl

[4] Smirnov V. A., Tolokonnikov G. K., Shondin Yu. G., EChAYa, 14:5 (1983), 1030–1062 | MR

[5] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 2, Mir, M., 1978 | MR

[6] Berezin F. A., Matem. sb., 60(102) (1963), 425–446 | MR

[7] Pontryagin L. S., Izv. AN SSSR, ser. matem., 8 (1944), 243–280 | Zbl

[8] Krein M. G., Langer G. K., DAN SSSR, 152:1 (1963), 39–42 | MR | Zbl

[9] Bognar J., Indefinite inner product spaces, Springer-Verlag, Berlin–Heidelberg–New York, 1974 | MR | Zbl

[10] Krein M. G., Langer G. K., Funkts. analiz i ego prilozh., 5:2 (1971), 59–71 | MR | Zbl

[11] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl