Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 22 (1988) no. 4, pp. 11-22.

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

@article{FAA_1988_22_4_a1,
     author = {R. G. Novikov},
     title = {Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {11--22},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1988_22_4_a1/}
}
TY  - JOUR
AU  - R. G. Novikov
TI  - Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1988
SP  - 11
EP  - 22
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1988_22_4_a1/
LA  - ru
ID  - FAA_1988_22_4_a1
ER  - 
%0 Journal Article
%A R. G. Novikov
%T Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1988
%P 11-22
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1988_22_4_a1/
%G ru
%F FAA_1988_22_4_a1
R. G. Novikov. Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 22 (1988) no. 4, pp. 11-22. http://geodesic.mathdoc.fr/item/FAA_1988_22_4_a1/

[1] Marchenko V.A., Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[2] Shadan K., Sabate P., Obratnye zadachi v kvantovoi teorii rasseyaniya, Mir, M., 1980 | MR

[3] Levitan B.M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[4] Berezanskii Yu.M., “O teoreme edinstvennosti v obratnoi zadache spektralnogo analiza dlya uravneniya Shredingera”, Trudy MMO, 7, 1958, 3–62 | MR

[5] Moses H.E., “Calculation of the scattering potential from reflection coefficients”, Phys. Rev., 102 (1956), 559–597 | DOI | MR

[6] Faddeev L.D., “Edinstvennost resheniya obratnoi zadachi rasseyaniya”, Vestnik LGU, 1956, no. 7, 126–130 | MR

[7] Lavrentev M.M., “Ob obratnoi zadache dlya volnovogo uravneniya”, DAN SSSR, 157:3 (1964), 520–521 | MR

[8] Faddeev L.D., “Rastuschie resheniya uravneniya Shredingera”, DAN SSSR, 165:3 (1965), 514–517 | Zbl

[9] Faddeev L.D., “Obratnaya zadacha kvantovoi teorii rasseyaniya. II”, Sovr. problemy matematiki, 3, VINITI, M., 1974, 93–180 | MR

[10] Newton R.G., “The Gelfand–Levitan method in the inverse scattering problems”, Scattering theory in mathematical physics, J.A. Lavita and J.P. Marchande editors, Reidel Publ. Co., Dordrecht, 1974, 193–235 | DOI

[11] Dubrovin B.A., Krichever I.M., Novikov S.P., “Uravnenie Shredingera v periodicheskom pole i rimanovy poverkhnosti”, DAN SSSR, 229:1 (1976), 15–18 | MR | Zbl

[12] Romanov V.G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR

[13] Newton R.G., “The Marchenko and Gel'fand-Levitan methods in the inverse scattering problem in one and three dimensions”, Conference on Inverse Scattering: Theory and Application, ed. J.B. Bednaretal, SIAM, Philadelphia, 1983, 1–74 | MR

[14] Fokas A.S., Ablowitz M.J., “On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane”, J. Math. Phys., 25 (1984), 2494–2505 | DOI | MR | Zbl

[15] Veselov A.Ya., Novikov S.P., “Konechnozonnye dvumernye operatory Shredingera. Vydelenie potentsialnykh operatorov. Veschestvennaya teoriya”, DAN SSSR, 279:4 (1984), 784–788 | MR | Zbl

[16] Nachman A.I., Ablowitz M.J., “A multidimensional inverse scattering method”, Studies in applied mathematics, 71 (1984), 243–250 | DOI | MR | Zbl

[17] Beals R., Coifman R.R., “Multidimensional scattering and nonlinear partial differential equations”, Proc. of Symposia in Pure Mathematics, 43 (1985), 45–70 | DOI | MR | Zbl

[18] Grinevich P.G., Novikov P.G., “Analogi mnogosolitonnykh potentsialov dlya dvumernogo operatora Shredingera i nelokalnaya zadacha Rimana”, DAN SSSR, 286:1 (1986), 19–22 | MR | Zbl

[19] Novikov R.G., “Postroenie dvumernogo operatora Shredingera s dannoi amplitudoi rasseyaniya pri fiksirovannoi energii”, TMF, 66:2 (1986), 234–240 | MR | Zbl

[20] Grinevich P.G., Manakov S.V., “Obratnaya zadacha teorii rasseyaniya dlya dvumernogo operatora Shredingera, $\partial$-metod i nelineinye uravneniya”, Funktsion. analiz i ego pril., 20:2 (1986), 14–24 | MR | Zbl

[21] Novikov R.G., “Vosstanovlenie dvumernogo operatora Shredingera po amplitude rasseyaniya pri fiksirovannoi energii”, Funktsion. analiz i ego pril., 20:3 (1986), 90–91 | MR | Zbl

[22] Fokas A.S., “An inverse problem for multidimensional first-order systems”, J. Math. Phys., 27 (1986), 1737–1746 | DOI | MR | Zbl

[23] Novikov P.G., Khenkin G.M., $\partial$-uravnenie v mnogomernoi obratnoi zadache rasseyaniya, Preprint No 27M, Institut fiziki, Krasnoyarsk, 1986, 1–36; УМН, 42:3 (1987), 93–152 | MR | Zbl

[24] Henkin G.M., Novikov R.G., “A multidimensional inverse problem in quantum and acoustic scattering”, Inverse Problems, 4 (1988), 103–121 | DOI | MR | Zbl

[25] Grinevich P.G., Novikov S.P., “Dvumernaya «obratnaya zadacha rasseyaniya» dlya otritsatelnykh energii i obobschenno analiticheskie funktsii. I. Energii nizhe osnovnogo sostoyaniya”, Funktsion. analiz i ego pril., 22:1 (1988), 23–33 | MR | Zbl

[26] Gelfand I.M., “Nekotorye voprosy funktsionalnogo analiza i algebry”, Mezhdunarodnyi matematicheskii kongress v Amsterdame, 1954 g., Nauka, M., 1961, 49–74

[27] Belishev M.I., “Ob odnom podkhode k mnogomernym obratnym zadacham dlya volnovogo uravneniya”, DAN SSSR, 297:3 (1987), 523–526

[28] Sylvester J. , Uhlmann G., “A uniqueness theorem for an inverse boundary value problem in electrical prospection”, Comm. Pure Appl. Math., 32 (1986), 91–112 | DOI | MR

[29] Sylvester J., Uhlmann G., “A global uniqueness theorem”, Ann. of Math., 125 (1987), 153–169 | DOI | MR | Zbl

[30] Calderon A.P., On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasileira de Matematica, Rio de Janerio, 1980 | MR

[31] Kohn R., Vogelius M., “Determining conductivity by boundary measurements. II. Interior Results”, Comm. Pure Appl. Math., 38 (1985), 643–667 | DOI | MR | Zbl