- Previous Article
- MCRF Home
- This Issue
-
Next Article
Local exact controllability to positive trajectory for parabolic system of chemotaxis
Counting function for interior transmission eigenvalues
1. | Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France |
References:
[1] |
S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand Mathematical Studies, No. 2, 1965. |
[2] |
F. Cakoni, M. Çayören and D. Colton, Transmission eigenvalues and the nondestructive testing of dielectrics, Inverse Problems, 24 (2008), 065016, 15pp.
doi: 10.1088/0266-5611/24/6/065016. |
[3] |
F. Cakoni, D. Colton and H. Haddar, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), 145-162.
doi: 10.1137/090754637. |
[4] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[5] |
F. Cakoni and H. Haddar, Transmission Eigenvalues in Inverse Scattering Theory, in Inverse Problems and Applications: Inside Out II, MSRI Publication, 60 (2013), 529-580. |
[6] |
H. Cartan, Théorie Élémentaire Des Fonctions Analytiques,, Hermann., ().
|
[7] |
D. Colton, A. Kirsch and L. Päivärinta, Far-field patterns for acoustic waves in an inhomogeneous medium, SIAM J. Math. Anal., 20 (1989), 1472-1483.
doi: 10.1137/0520096. |
[8] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-662-02835-3. |
[9] |
M. Dimassi and V. Petkov, Upper bound for the counting function of interior transmission eigenvalues,, preprint, ().
|
[10] |
M. Faierman, Transmission eigenvalues for parameter-elliptic boundary problems,, preprint., ().
|
[11] |
M. Hitrik, K. Krupchyk, P. Ola Petri and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, SIAM J. Math. Anal., 42 (2010), 2965-2986.
doi: 10.1137/100793748. |
[12] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for elliptic operators, SIAM J. Math. Anal., 43 (2011), 2630-2639.
doi: 10.1137/110827867. |
[13] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, The interior transmission problem and bounds on transmission eigenvalues, Math. Res. Lett., 18 (2011), 279-293.
doi: 10.4310/MRL.2011.v18.n2.a7. |
[14] |
J. Karamata, Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze, Math. Z., 33 (1931), 294-299.
doi: 10.1007/BF01174355. |
[15] |
E. Lakshtanov and B. Vainberg, Ellipticity in the interior transmission problem in anisotropic media, SIAM J. Math. Anal., 44 (2012), 1165-1174.
doi: 10.1137/11084738X. |
[16] |
E. Lakshtanov and B. Vainberg, Remarks on interior transmission eigenvalues, Weyl formula and branching billiards, J. Phys. A: Math. Theor, 45 (2012), 125202, 10pp.
doi: 10.1088/1751-8113/45/12/125202. |
[17] |
E. Lakshtanov and B. Vainberg, Bounds on positive interior transmission eigenvalues, Inverse Problems, 28 (2012), 105005, 13pp.
doi: 10.1088/0266-5611/28/10/105005. |
[18] |
E. Lakshtanov and B. Vainberg, Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem, Inverse Problems, 29 (2013), 104003, 19pp.
doi: 10.1088/0266-5611/29/10/104003. |
[19] |
P. Malliavin, Un théorème taubérien relié aux estimations de valeurs propres,, Séminaire Jean Leray, (): 1962.
|
[20] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753.
doi: 10.1137/070697525. |
[21] |
H. Pham and P. Stefanov, Weyl asymptotics of the transmission eigenvalues for a constant index of refraction, Inverse Problems and Imaging, 8 (2014), 795-810.
doi: 10.3934/ipi.2014.8.795. |
[22] |
L. Robbiano, Spectral analysis on interior transmission eigenvalues, Inverse Problems, 29 (2013), 104001, 28pp.
doi: 10.1088/0266-5611/29/10/104001. |
[23] |
J. Sylvester, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), 341-354.
doi: 10.1137/110836420. |
show all references
References:
[1] |
S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand Mathematical Studies, No. 2, 1965. |
[2] |
F. Cakoni, M. Çayören and D. Colton, Transmission eigenvalues and the nondestructive testing of dielectrics, Inverse Problems, 24 (2008), 065016, 15pp.
doi: 10.1088/0266-5611/24/6/065016. |
[3] |
F. Cakoni, D. Colton and H. Haddar, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), 145-162.
doi: 10.1137/090754637. |
[4] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[5] |
F. Cakoni and H. Haddar, Transmission Eigenvalues in Inverse Scattering Theory, in Inverse Problems and Applications: Inside Out II, MSRI Publication, 60 (2013), 529-580. |
[6] |
H. Cartan, Théorie Élémentaire Des Fonctions Analytiques,, Hermann., ().
|
[7] |
D. Colton, A. Kirsch and L. Päivärinta, Far-field patterns for acoustic waves in an inhomogeneous medium, SIAM J. Math. Anal., 20 (1989), 1472-1483.
doi: 10.1137/0520096. |
[8] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-662-02835-3. |
[9] |
M. Dimassi and V. Petkov, Upper bound for the counting function of interior transmission eigenvalues,, preprint, ().
|
[10] |
M. Faierman, Transmission eigenvalues for parameter-elliptic boundary problems,, preprint., ().
|
[11] |
M. Hitrik, K. Krupchyk, P. Ola Petri and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, SIAM J. Math. Anal., 42 (2010), 2965-2986.
doi: 10.1137/100793748. |
[12] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for elliptic operators, SIAM J. Math. Anal., 43 (2011), 2630-2639.
doi: 10.1137/110827867. |
[13] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, The interior transmission problem and bounds on transmission eigenvalues, Math. Res. Lett., 18 (2011), 279-293.
doi: 10.4310/MRL.2011.v18.n2.a7. |
[14] |
J. Karamata, Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze, Math. Z., 33 (1931), 294-299.
doi: 10.1007/BF01174355. |
[15] |
E. Lakshtanov and B. Vainberg, Ellipticity in the interior transmission problem in anisotropic media, SIAM J. Math. Anal., 44 (2012), 1165-1174.
doi: 10.1137/11084738X. |
[16] |
E. Lakshtanov and B. Vainberg, Remarks on interior transmission eigenvalues, Weyl formula and branching billiards, J. Phys. A: Math. Theor, 45 (2012), 125202, 10pp.
doi: 10.1088/1751-8113/45/12/125202. |
[17] |
E. Lakshtanov and B. Vainberg, Bounds on positive interior transmission eigenvalues, Inverse Problems, 28 (2012), 105005, 13pp.
doi: 10.1088/0266-5611/28/10/105005. |
[18] |
E. Lakshtanov and B. Vainberg, Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem, Inverse Problems, 29 (2013), 104003, 19pp.
doi: 10.1088/0266-5611/29/10/104003. |
[19] |
P. Malliavin, Un théorème taubérien relié aux estimations de valeurs propres,, Séminaire Jean Leray, (): 1962.
|
[20] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753.
doi: 10.1137/070697525. |
[21] |
H. Pham and P. Stefanov, Weyl asymptotics of the transmission eigenvalues for a constant index of refraction, Inverse Problems and Imaging, 8 (2014), 795-810.
doi: 10.3934/ipi.2014.8.795. |
[22] |
L. Robbiano, Spectral analysis on interior transmission eigenvalues, Inverse Problems, 29 (2013), 104001, 28pp.
doi: 10.1088/0266-5611/29/10/104001. |
[23] |
J. Sylvester, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), 341-354.
doi: 10.1137/110836420. |
[1] |
Ha Pham, Plamen Stefanov. Weyl asymptotics of the transmission eigenvalues for a constant index of refraction. Inverse Problems and Imaging, 2014, 8 (3) : 795-810. doi: 10.3934/ipi.2014.8.795 |
[2] |
Vesselin Petkov, Georgi Vodev. Localization of the interior transmission eigenvalues for a ball. Inverse Problems and Imaging, 2017, 11 (2) : 355-372. doi: 10.3934/ipi.2017017 |
[3] |
Fioralba Cakoni, Drossos Gintides. New results on transmission eigenvalues. Inverse Problems and Imaging, 2010, 4 (1) : 39-48. doi: 10.3934/ipi.2010.4.39 |
[4] |
Andreas Kirsch. On the existence of transmission eigenvalues. Inverse Problems and Imaging, 2009, 3 (2) : 155-172. doi: 10.3934/ipi.2009.3.155 |
[5] |
Dmitry Jakobson and Iosif Polterovich. Lower bounds for the spectral function and for the remainder in local Weyl's law on manifolds. Electronic Research Announcements, 2005, 11: 71-77. |
[6] |
David Colton, Lassi Päivärinta, John Sylvester. The interior transmission problem. Inverse Problems and Imaging, 2007, 1 (1) : 13-28. doi: 10.3934/ipi.2007.1.13 |
[7] |
Armin Lechleiter. The factorization method is independent of transmission eigenvalues. Inverse Problems and Imaging, 2009, 3 (1) : 123-138. doi: 10.3934/ipi.2009.3.123 |
[8] |
Yalin Zhang, Guoliang Shi. Continuous dependence of the transmission eigenvalues in one dimension. Inverse Problems and Imaging, 2015, 9 (1) : 273-287. doi: 10.3934/ipi.2015.9.273 |
[9] |
Fioralba Cakoni, Anne Cossonnière, Houssem Haddar. Transmission eigenvalues for inhomogeneous media containing obstacles. Inverse Problems and Imaging, 2012, 6 (3) : 373-398. doi: 10.3934/ipi.2012.6.373 |
[10] |
Fioralba Cakoni, Shixu Meng, Jingni Xiao. A note on transmission eigenvalues in electromagnetic scattering theory. Inverse Problems and Imaging, 2021, 15 (5) : 999-1014. doi: 10.3934/ipi.2021025 |
[11] |
Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems and Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487 |
[12] |
Fioralba Cakoni, Shari Moskow, Scott Rome. The perturbation of transmission eigenvalues for inhomogeneous media in the presence of small penetrable inclusions. Inverse Problems and Imaging, 2015, 9 (3) : 725-748. doi: 10.3934/ipi.2015.9.725 |
[13] |
Jun Zhang, Xinyue Fan. An efficient spectral method for the Helmholtz transmission eigenvalues in polar geometries. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4799-4813. doi: 10.3934/dcdsb.2019031 |
[14] |
Fioralba Cakoni, Shari Moskow, Scott Rome. Asymptotic expansions of transmission eigenvalues for small perturbations of media with generally signed contrast. Inverse Problems and Imaging, 2018, 12 (4) : 971-992. doi: 10.3934/ipi.2018041 |
[15] |
Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems and Imaging, 2021, 15 (3) : 445-474. doi: 10.3934/ipi.2020075 |
[16] |
Fioralba Cakoni, Houssem Haddar. A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media. Inverse Problems and Imaging, 2007, 1 (3) : 443-456. doi: 10.3934/ipi.2007.1.443 |
[17] |
Yuebin Hao. Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1387-1397. doi: 10.3934/cpaa.2020068 |
[18] |
Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems and Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159 |
[19] |
Uri Bader, Alex Furman. Boundaries, Weyl groups, and Superrigidity. Electronic Research Announcements, 2012, 19: 41-48. doi: 10.3934/era.2012.19.41 |
[20] |
Frédéric Naud, Anke Pohl, Louis Soares. Fractal Weyl bounds and Hecke triangle groups. Electronic Research Announcements, 2019, 26: 24-35. doi: 10.3934/era.2019.26.003 |
2020 Impact Factor: 1.284
Tools
Metrics
Other articles
by authors
[Back to Top]