Skip to main content
Log in

Projecting and resolving operators of a periodic waveguide

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

A dielectric periodic waveguide with almost arbitrary smooth boundary is studied. The existence of projecting and resolving operators is established. Bibliography: 9 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. I. Derguzov and I. V. Denisova, “The characteristic spectrum of the reduced wave equation with periodic coefficients in the three-dimensional space”[in Russian], Probl. Mat. Anal. 21 (2000), 110–137; English transl.: J. Math. Sci., New York 105 (2001), no. 5, 2377–2397.

    MATH  Google Scholar 

  2. V. I. Derguzov and I. V. Denisova, “Invariant subspaces of three-dimensional periodic lightguides” [in Russian], Probl. Mat. Anal. 23 (2001), 3–13; English transl.: J. Math. Sci., New York 107 (2001), no. 3, 3807–3814.

    MATH  Google Scholar 

  3. I. V. Denisova, “Resolving operators for a three-dimensional periodic waveguide” [in Russian], Probl. Mat. Anal. 26 (2003), 67–86; English transl.: J. Math. Sci., New York 117 (2003), no. 3, 4109–4121.

    MATH  Google Scholar 

  4. V. I. Derguzov and I. V. Denisova, “Projecting and resolving operators for a three-dimensional waveguide” [in Russian], Probl. Mat. Anal. 30 (2005), 31–45; English transl.: J. Math. Sci., New York, 128 (2005), no. 5, 3195–3213.

    MATH  Google Scholar 

  5. V. I. Derguzov and I. V. Denisova, “Spreading waves in a three-dimensional dielectric periodic waveguide described by the generalized reduced wave equation” [in Russian], Probl. Mat. Anal. 29 (2004), 17–24; English transl.: J. Math. Sci., New York 124 (2004), no. 3

    MATH  Google Scholar 

  6. V. I. Derguzov and I. V. Denisova, “Projection operators of a three-dimensional periodic waveguide” [in Russian], Probl. Mat. Anal. 26 (2003), 87–139; English transl.: J. Math. Sci., New York 117 (2003), no. 3, 4122-4156.

    MATH  Google Scholar 

  7. O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973); English transl. of the 1st ed.: Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).

    Google Scholar 

  8. J.-L. Lions and E. Magenes, Nonhomogeneous Boundary-Value Problems and Applications, Berlin, Springer-Verlag (1972).

    Google Scholar 

  9. V. I. Derguzov and I. V. Denisova, “The problem about wave drop on the junction of two periodic dielectric waveguides” [in Russian] Vestnik St.Peterb. Gos. Univ, Ser. 1 (2006), no. 3, 27–33.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 47–57

Rights and permissions

Reprints and permissions

About this article

Cite this article

Derguzov, V.I. Projecting and resolving operators of a periodic waveguide. J Math Sci 144, 4581–4591 (2007). https://doi.org/10.1007/s10958-007-0296-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0296-x

Keywords

Navigation