The operator with the Dirichlet boundary condition is considered in a parallelepiped. The problem of restoring from positions of nodal surfaces is solved.
@article{SEDP_1997-1998____A1_0, author = {Karpeshina, Yu E. and McLaughlin, J. R.}, title = {Two {Methods} of {Solution} of the {Three-Dimensional} {Inverse} {Nodal} {Problem.}}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:1}, pages = {1--9}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {1997-1998}, zbl = {1061.35527}, mrnumber = {1660514}, language = {en}, url = {http://www.numdam.org/item/SEDP_1997-1998____A1_0/} }
TY - JOUR AU - Karpeshina, Yu E. AU - McLaughlin, J. R. TI - Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem. JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:1 PY - 1997-1998 SP - 1 EP - 9 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_1997-1998____A1_0/ LA - en ID - SEDP_1997-1998____A1_0 ER -
%0 Journal Article %A Karpeshina, Yu E. %A McLaughlin, J. R. %T Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem. %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:1 %D 1997-1998 %P 1-9 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_1997-1998____A1_0/ %G en %F SEDP_1997-1998____A1_0
Karpeshina, Yu E.; McLaughlin, J. R. Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 1, 9 p. http://www.numdam.org/item/SEDP_1997-1998____A1_0/
[HM] O.H. Hald, J.R. McLaughlin Inverse Nodal problems: Finding the Potential from Nodal lines. Memoirs of the AMS, 119, # 572, 1997, 148 pp. | MR | Zbl
[K] Yu. E. Karpeshina Perturbation theory for the Schrödinger operator with a periodic potential, in series “Lecture Notes in Mathematics", # 1663, Springer-Verlag, 1997, 352 pp. | Zbl