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Investigation of a spectral problem for the Helmholtz operator on the plane

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References

  1. Snyder, A. and Love, J.,Teoriya opticheskikh volnovodov (Theory of Optical Waveguides), Moscow, 1987.

  2. Sodha, M.S. and Gkhatak, A.K.,Neodnorodnye opticheskie volnovody (Inhomogeneous Optical Waveg-uides), Moscow, 1980.

  3. Shevchenko, V.V.,Radiotekhnika i Elektronika, 1974, vol. 19, no. 3, pp. 473–480.

    Google Scholar 

  4. Voitovich, N.N., Katsenelenbaum, B.Z., Sivov, A.N., and Shatrov, A.D.,Radiotekhnika i Elektronika, 1979, vol. 24, no. 7, pp. 1245–1263.

    Google Scholar 

  5. Sveshnikov, A.G., inVychislit. metody i programmirovanie (Computational Methods and Program-ming), Moscow, 1969, issue 13, pp. 145–151.

  6. Reichardt, H.,Abh. Mathem. Seminar. Univ. Hamburg, 1960, vol. 24, pp. 41–53.

    MATH  MathSciNet  Google Scholar 

  7. Shestopalov, V.P.,Spektral’naya teoriya i vozbuzhdenie otkrytykh Struktur (Spectral Theory and Exci-tation of Open Structures), Kiev, 1987.

  8. Il’inskii, A.S. and Shestopalov, Yu.V.,Primenenie metodov spektral’noi teorii v zadachakh rasprostra-neniya voln (Application of Methods of Spectral Theory to Wave Propagation Problems), Moscow, 1989.

  9. Nosich, A.I.,J. El. Wav. Appl., 1994, vol. 8, no. 3, pp. 329–353.

    Google Scholar 

  10. Karchevskii, E.M., inIssledovaniya po prikladnoi matematike (Investigations in Applied Mathematics), Kazan, 1997, issue 22, pp. 47–51.

  11. Karchevskii, E.M.,Izv. Vyssh. Uchebn. Zaved. Matematika, 1999, no. 1, pp. 10–17.

  12. Gokhberg, I.Ts. and Krein, M.G.,Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gil ’bertovom prostranstve (Introduction to the Theory of Linear Nonself-Adjoint Operators in a Hilbert Space), Moscow, 1965.

  13. Dautov, R.Z., Lyashko, A.D., and Solov’ev, S.I.,Differents. Uravn., 1991, vol. 27, no. 7, pp. 1144–1153.

    MATH  MathSciNet  Google Scholar 

  14. Il’inskii, A.S., Kravtsov, V.V., and Sveshnikov, A.G.,Matematicheskie modeli elektrodinamiki (Mathe-matical Models of Electrodynamics), Moscow, 1991.

  15. Jahnke, E., Emde, F., and Losch, F.,Tables of Higher Functions, New York: McGraw-Hill; Stuttgart: Teubner, 1960. Translated under the titleSpetsial’nye funktsii, Moscow, 1968.

    MATH  Google Scholar 

  16. Vekua, I.N.,Tr. Tbil. Mat. In-ta, 1943, vol. 12, pp. 105–174.

    Google Scholar 

  17. Vladimirov, V.S.,Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow, 1976.

  18. Nikiforov, A.F. and Uvarov, V.B.,Osnovy teorii spetsial’nykh funktsii (Foundations of Theory of Special Functions), Moscow, 1974.

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Karchevskii, E.M., Solov’ev, S.I. Investigation of a spectral problem for the Helmholtz operator on the plane. Diff Equat 36, 631–634 (2000). https://doi.org/10.1007/BF02754261

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