TY - JOUR
T1 - On the determination of Dirichlet or transmission eigenvalues from far field data
AU - Cakoni, Fioralba
AU - Colton, David
AU - Haddar, Houssem
N1 - Funding Information:
✩ The research of F.C. and D.C. was supported in part by the U.S. Air Force Office of Scientific Research under Grant FA-9550-08-1-0138. This research was in part supported by the associate team ISIP of INRIA-UDEL. E-mail addresses: [email protected] (F. Cakoni), [email protected] (D. Colton), [email protected] (H. Haddar).
PY - 2010/4
Y1 - 2010/4
N2 - We show that the Herglotz wave function with kernel the Tikhonov regularized solution of the far field equation becomes unbounded as the regularization parameter tends to zero iff the wavenumber k belongs to a discrete set of values. When the scatterer is such that the total field vanishes on the boundary, these values correspond to the square root of Dirichlet eigenvalues for -Δ. When the scatterer is a nonabsorbing inhomogeneous medium these values correspond to so-called transmission eigenvalues.
AB - We show that the Herglotz wave function with kernel the Tikhonov regularized solution of the far field equation becomes unbounded as the regularization parameter tends to zero iff the wavenumber k belongs to a discrete set of values. When the scatterer is such that the total field vanishes on the boundary, these values correspond to the square root of Dirichlet eigenvalues for -Δ. When the scatterer is a nonabsorbing inhomogeneous medium these values correspond to so-called transmission eigenvalues.
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U2 - 10.1016/j.crma.2010.02.003
DO - 10.1016/j.crma.2010.02.003
M3 - Article
AN - SCOPUS:77949491426
SN - 1631-073X
VL - 348
SP - 379
EP - 383
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 7-8
ER -