Weyl asymptotics of the transmission eigenvalues for a constant index of refraction

We prove Weyl type of asymptotic formulas for the real and the complex internal transmission eigenvalues when the domain is a ball and the index of refraction is constant.

[1]  Georgi Vodev,et al.  Asymptotics of the number of the interior transmission eigenvalues , 2014, 1403.3949.

[2]  Joyce R. McLaughlin,et al.  On the Uniqueness of a Spherically Symmetric Speed of Sound from Transmission Eigenvalues , 1994 .

[3]  Transmission Eigenvalues in One Dimension , 2013, 1305.0733.

[4]  Maciej Zworski,et al.  Distribution of poles for scattering on the real line , 1987 .

[5]  Petri Ola,et al.  Transmission Eigenvalues for Elliptic Operators , 2010, SIAM J. Math. Anal..

[6]  Evgeny Lakshtanov,et al.  Bounds on positive interior transmission eigenvalues , 2012, 1206.3782.

[7]  E. C. Titchmarsh The Zeros of Certain Integral Functions , 1926 .

[8]  Fioralba Cakoni,et al.  On the interior transmission eigenvalue problem , 2010, Int. J. Comput. Sci. Math..

[9]  Sharp upper bounds on the number of the scattering poles , 2004, math/0412536.

[10]  D. Colton,et al.  The interior transmission problem , 2007 .

[11]  David Colton,et al.  Qualitative Methods in Inverse Scattering Theory , 1997 .

[12]  Petri Ola,et al.  The interior transmission problem and bounds on transmission eigenvalues , 2010, 1009.5640.

[13]  Maciej Zworski,et al.  Complex scaling and the distribution of scattering poles , 1991 .

[14]  Peter Monk,et al.  The Linear Sampling Method in Inverse Electromagnetic Scattering , 2010 .

[15]  John Sylvester,et al.  Transmission eigenvalues for degenerate and singular cases , 2012 .

[16]  Fioralba Cakoni,et al.  Transmission Eigenvalues , 2021, Applied Mathematical Sciences.

[17]  John Sylvester,et al.  Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators , 2011, SIAM J. Math. Anal..

[18]  David Colton,et al.  Complex transmission eigenvalues for spherically stratified media , 2012 .

[19]  Evgeny Lakshtanov,et al.  Ellipticity in the Interior Transmission Problem in Anisotropic Media , 2012, SIAM J. Math. Anal..

[20]  David Colton,et al.  Dense sets and far field patterns for acoustic waves in an inhomogeneous medium , 1988, Proceedings of the Edinburgh Mathematical Society.

[21]  Fioralba Cakoni,et al.  Qualitative Methods in Inverse Scattering Theory: An Introduction , 2005 .

[22]  E. Lakshtanov,et al.  Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem , 2012, 1212.6785.

[23]  Petri Ola,et al.  Transmission Eigenvalues for Operators with Constant Coefficients , 2010, SIAM J. Math. Anal..

[24]  Andreas Kirsch,et al.  The Denseness of the Far Field Patterns for the Transmission Problem , 1986 .

[25]  Evgeny Lakshtanov,et al.  Remarks on interior transmission eigenvalues, Weyl formula and branching billiards , 2011, 1112.0891.

[26]  Fioralba Cakoni,et al.  The Existence of an Infinite Discrete Set of Transmission Eigenvalues , 2010, SIAM J. Math. Anal..

[27]  D. Colton,et al.  THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM , 1988 .

[28]  N I Grinberg,et al.  The Factorization Method for Inverse Problems , 2007 .

[29]  F. Olver Asymptotics and Special Functions , 1974 .

[30]  Mouez Dimassi,et al.  Upper bound for the counting function of interior transmission eigenvalues , 2013, 1308.2594.

[31]  Counting function for interior transmission eigenvalues , 2013, 1310.6273.