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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 8
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Articles

An uniqueness result with some density theorems with interior transmission eigenvalues

Pages 1527-1544 | Received 26 Mar 2013, Accepted 14 Oct 2013, Published online: 10 Jul 2014

References

  • Colton D, Monk P. The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium. Q. J. Mech. appl. Math. 1988;41:97–125.
  • Colton D, Päivärinta L, Sylvester J. The interior transmission problem. Inverse Probl. Imag. 2007;1:13–28.
  • Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 2nd ed. Vol. 93, Applied mathematical science. Berlin: Springer-Verlag; 1998.
  • Cakoni F, Colton D, Haddar H. The interior transmission eigenvalue problem for absorbing media. Inverse Probl. 2012;28:045005.
  • Cakoni F, Colton D, Gintides D. The interior transmission eigenvalue problem. SIAM J. Math. Anal. 2010;42:2912–2921.
  • Kirsch A. On the existence of transmission eigenvalues. Inverse probl. Imag. 2009;3:155–172.
  • McLaughlin JR, Polyakov PL. On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. J. Differ. Equ. 1994;107:351–382.
  • Aktosun T, Gintides D, Papanicolaou VG. The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Probl. 2011;27:115004.
  • Pöschel J, Trubowitz E. Inverse spectral theory. Orlando: Academic Press; 1987.
  • Leung Y-J, Colton D. Complex transmission eigenvalues for spherically stratified media. Inverse probl. 2012;28:075005.
  • Erdelyi A. Asymptotics expansions. New York (NY): Dover; 1956.
  • Dickson DG. Zeros of exponential sums. Proc. Amer. Math. Soc. 1965;16:84–89.
  • Dickson DG. Expansions in series of solutions of linear difference-differential and infinite order differential equations with constant coefficients. Vol. 23. Providence (RI): Memoirs of the American Mathematical Society; 1957.
  • Langer RE. On the zeros of exponential sums and integrals. Bull. Amer. Math. Soc. 1931;37:213–239.
  • Levin BJa. Distribution of zeros of entire functions. revised edition. Translations of mathematical monographs. Providence (RI): American mathematical society; 1972.
  • Levin BJa. Lectures on entire functions. Vol. 150, Translation of mathematical monographs. Providence (RI): AMS; 1996.
  • Cartwright ML. On the directions of Borel of functions which are regular and of finite order in an angle. Proc. London Math. Soc. Ser. 2. 1933;38:503–541.
  • Cartwright ML. Integral functions. New York (NY): Cambridge University Press; 1956.
  • Boas RP Jr. Entire functions. New York (NY): Academic Press; 1954.
  • Koosis P. The logarithmic integral I. Cambridge: Cambridge University Press; 1997.
  • McLaughlin JR. Inverse spectral theory using nodal points as data-a uniqueness result. J. Differ. Equ. 1988;73:354–362.

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