The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 307-327.
@article{COCV_1997__2__307_0,
     author = {Belishev, M. I. and Gotlib, V. Yu. and Ivanov, S. A.},
     title = {The {BC-method} in multidimensional spectral inverse problem : theory and numerical illustrations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {307--327},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1997},
     mrnumber = {1474105},
     zbl = {0901.65085},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1997__2__307_0/}
}
TY  - JOUR
AU  - Belishev, M. I.
AU  - Gotlib, V. Yu.
AU  - Ivanov, S. A.
TI  - The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1997
SP  - 307
EP  - 327
VL  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_1997__2__307_0/
LA  - en
ID  - COCV_1997__2__307_0
ER  - 
%0 Journal Article
%A Belishev, M. I.
%A Gotlib, V. Yu.
%A Ivanov, S. A.
%T The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1997
%P 307-327
%V 2
%I EDP-Sciences
%U http://www.numdam.org/item/COCV_1997__2__307_0/
%G en
%F COCV_1997__2__307_0
Belishev, M. I.; Gotlib, V. Yu.; Ivanov, S. A. The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 307-327. http://www.numdam.org/item/COCV_1997__2__307_0/

[1] Avdonin S. A., Belishev M. I., Ivanov S. A.: The controllability in a filled domain for multidimensional wave equation with a singular boundary control. Zap. Nauch. Sem. POMI, 210 (23), 1994, 7-21 (in Russian). | MR | Zbl

[2] Bardos C., Belishev M.I.: The Wave Shaping Problem. Proceedings of the Colloquium in the Memory of P. Grisvard, Paris, December 1994. | Zbl

[3] Bardos C., Lebeau G., Rauch J.: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control and Optimization, 30 (5), 1992, 1024-1065. | MR | Zbl

[4] Bateman H., Erdelyi A.: Higher Transcendental Functions. V.3, N.Y., Mc Graw Hill, 1955. | MR | Zbl

[5] Belishev M.I.: An approach to multidimensional inverse problems for the wave equation. Dokl. Akad. Nauk SSSR, 297 (3), 1987, 524-527; English transl. in Soviet Math. Dokl. 36 (3), 1988, 481-484. | MR | Zbl

[6] Belishev M.I.: Wave bases in multidimensional inverse problems. Math. USSR Sbornik, 180 (5), 1989, 584-602. | MR | Zbl

[7] Belishev M.I.: Boundary control and wave field continuation. Preprint POMI P-l-90, 1990, 1-41 (in Russian).

[8] Belishev M.I., Kachalov A.P.: Boundary control and quasiphotons in the problem of reconstruction of a Riemannian manifold via dynamical data. Zapiski Nauchn. Seminarov POMI, 203 (22), 1992, 21-50 (in Russian). | MR | Zbl

[9] Belishev M.I., Kachalov A.P.: An operator integral in multidimensional spectral Inverse Problem. Zapiski Nauchn. Seminarov POMI, 215 (14), 1994, 9-37 (in Russian). | Zbl

[10] Belishev M.I., Kurylev Ya.V.: Boundary control, wave field continuation and inverse problems for the wave equation. Computer Math. Applic., 22, (4-5), 1991, 27-52. | MR | Zbl

[11] Belishev M.I., Kurylev Ya.V.: To a reconstruction of a Riemannian manifold via its spectral data (BC-method). Comm. PDE, 17, (5-6), 1992, 767-804. | MR | Zbl

[12] Belishev M.I., Ryzhov V.A., Filippov V.B.: Spectral variant of the BC-method: theory and numerical testing. Dokl. Ross. Akad. Nauk, 332 (4), 1994, 414-417. English translation in POMI Preprint 1-1994. | MR | Zbl

[13] Berezanskii Yu. M.: To the uniqueness in the inverse spectral problem for Schrödinger operator. Proceedings of Moscow Math. Soc. 7 (3) 1958, 3-51 (in Russian).

[14] Gromol D., Klingenberg W., Meyer W.: Riemannsche Geometrie im Grossen. Springer-Verlag, 1968. | MR | Zbl

[15] Hartman P.: Geodesic parallel coordinates in the large. Amer. Math. Soc., 86 (4), 1964, 705-727. | MR | Zbl

[16] Hörmander L.: The Analysis of Linear Partial Differential Operators III. Pseudo-Differential Operators. Springer-Verlag, 1985. | Zbl

[17] Hörmander L.: A uniqueness theorem for second order hyperbolic differential equation. Comm. PDE, 17 (5-6), 1992, 699-314. | MR | Zbl

[18] Krein M.G.: On one method of efficient solving of inverse problem. Dokl. Akad. Nauk SSSR, 94 (6), 1954, 987-990 (in Russian). | MR

[19] Lasiecka I., Lions J.-L., Triggiani R.: Nonhomogeneous boundary value problem for second order hyperbolic operator. J. Math. Pures et Appl. 65 (2), 1986, 149-192. | MR | Zbl

[20] Lions J.-L.: Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. Dunod-Gauthier-Villars. Paris, 1968. | MR | Zbl

[21] Nachman R.: Reconstructions from boundary measurements. Ann. Math., 128, 1988, 531-576. | MR | Zbl

[22] Novikov R.: A multidimensional inverse spectral problem for the equation - ∆ ˉ + (v(x) - Eu(x))ˉ = 0, Funktsional, Anal. i Prilozhen, 22 (4), 1988, 11-22, translated in Functional Anal. Appl., 22 (4), 1988, 263-272. | MR | Zbl

[23] Novikov R., Henkin G.: ∂-equation in multidimensional inverse scattering problem, Uspekhi Matem Nauk, 42 (3), 1987, 94-152 (in Russian). Translated in Math. Surv., 42 (4), 1987, 109-180. | MR | Zbl

[24] Robbiano L.: Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques, Comm. PDE, 16 (4-5), 1991, 789-800. | MR | Zbl

[25] Russell D. L.: Controllability and stabilizability theory for linear partial differential equations. SIAM Review, 20 (4), 1978, 639-739. | MR | Zbl

[26] Sylvester J., Uhlmann G.: A uniqueness theorem for an inverse boundary value problem in electrical prospection, Comm. Pure Appl. Math., 39, 1986, 91-112. | MR | Zbl

[27] Tataru D.: Unique continuation for solutions of PDE's; between Hörmander's theorem and Holmgren's theorem. Comm. PDE, 20, 1995, 855-884. | MR | Zbl

[28] Wainberg B.R.: Asymptotic Methods in Equations of Mathematical Physics. Moscow, Nauka (in Russian), 1982. | Zbl