Skip to main content
Log in

Spectral analysis of the Transport Equation. I. Nondegenerate and multigroup case

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

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.

Literature

  1. H.Bart, I.Gohberg, M.A.Kaashoek: Minimal factorization of matrix and operator functions. Operator Theory: Advances and Applications 1, Birkhäuser Verlag, 1979.

  2. R.L.Bowden, S.Sancaktar, P.F.Zweifel: Multigroup neutron transport. I.Full range. Journal of Math.Physics, 17, 76–86, 1976.

    Article  Google Scholar 

  3. K.M.Case: Elementary solutions of the transport equation and their applications. Ann.Phys. (New York), 9, 1–23, 1960.

    Article  Google Scholar 

  4. N.Dunford, J.T.Schwarz: Linear Operators I, II. New York/London, Interscience, 1958.

    Google Scholar 

  5. I.A.Feldman: The radiative transport equation and operator Wiener-Hopf equations. Funct.Anal.Appl. 5, 262–264, 1971 = Funkcional.Anal. i Priložen. 5, no.3, 106–108, 1971 (Russian).

    Google Scholar 

  6. I.A.Feldman: Wiener-Hopf operator equations and their application to the transport equation. Integral Equations and Operator Theory 3, no. 1, 43–61, 1980 = Mat.Issled. 6, no. 3, 115–132, 1971 (Russian).

    Article  Google Scholar 

  7. I.A.Feldman: On an iteration method for the equation of radiant energy transfer. Soviet Math.Dokl. 12, no.4, 1034–1038, 1971 = Dokl.Adad.Nauk SSSR 199, no.1, 1971 (Russian).

    Google Scholar 

  8. I.A.Feldman: On some projection methods for the solution of the equation of radiative energy transport. Mat.Issled. 7, no. 4, 228–236, 1972 (Russian).

    Google Scholar 

  9. I.A.Feldman: On Wiener-Hopf equations with weakly integrable operator-valued kernels. Mat.Issled. 8, no. 4, 101–110, 1973 (Russian).

    Google Scholar 

  10. I.C.Gohberg, I.A.Feldman: Convolution equations and projection methods for their solution. Transl.Math. Monographs, vol. 41, A.M.S., Providence, R.I., 1974 = Moscow, "Nauka", 1971 (Russian).

    Google Scholar 

  11. I.C.Gohberg, M.G.Krein: Systems of integral equations on a half-line with kernels depending on the difference of arguments. A.M.S. Transl. 14, 217–287, 1960 = Uspehi Mat.Nauk 13, no. 2, 3–72 (Russian).

    Google Scholar 

  12. I.C.Gohberg, M.G.Krein: Introduction to the theory of linear non-selfadjoint operators in Hilbert space. Trans.Math.Monographs, vol. 18, A.M.S., Providence, R.I., 1969 = Moscow, "Nauka", 1965 (Russian).

    Google Scholar 

  13. I.C.Gohberg: The problem of factorization of operator functions. Izvestija Akad.Nauk SSSR, Serija Mat. 28, 1964, 1055–1082 (Russian).

    Google Scholar 

  14. I.C.Gohberg,J.Leiterer: Factorization of operator functions with respect to a contour. II. Canonical factorization of.operator functions, close to the identity. Math. Nachrichten 54, 41–74, 1972 (Russian).

    Google Scholar 

  15. I.C.Gohberg, J.Leiterer: Factorization of operator functions with respect to a contour. III. Factorization in algebras. Math. Nachrichten 55, 33–61, 1973 (Russian).

    Google Scholar 

  16. R.J.Hangelbroek: A functional analytic approach to the linear transport equation. Thesis, University of Groningen, the Netherlands, 1973.

    Google Scholar 

  17. R.J.Hangelbroek: On the derivation of some formulas in linear transport theory for media with anisotripic scattering. Report 7720, University of Nijmegen, the Netherlands, 1978.

    Google Scholar 

  18. R.J.Hangelbroek, C.G.Lekkerkerker: Decompositions of a Hilbert space and factorization of a W-A determinant. SIAM J.Math.Anal. 8, 458–472, 1977.

    Article  Google Scholar 

  19. L.V.Kantorovič, G.P.Akilov: Functional analysis in normed spaces. Series of Monographs in Pure and Appl.Math., vol 46, New York, Macmillan, 1964 = Moscow, Fizmatgiz, 1959 (Russian).

    Google Scholar 

  20. E.W.Larsen, G.J.Habetler: A functional analytic derivation of Case's full- and half-range formulas. Comm.Pure Appl.Math. 26, 525–537, 1973.

    Google Scholar 

  21. C.G.Lekkerkerker: On eigendistributions in linear transport theory. Proc.Royal Soc. Edinburgh, 83 A, 303–326, 1979.

    Google Scholar 

  22. N.J.Mc Cormick, I.Kuščer: Singular eigenfunction expansions in neutron transport theory. Advances in Nuclear Sci. Technology 7, 181–282, 1972.

    Google Scholar 

  23. M.H.Stone: Linear transformations in Hilbert space and their applications to analysis. Amer.Math.Soc. Colloquium Pub., New York, vol. 15, 1932.

    Google Scholar 

  24. M.M.R.Williams: The Wiener-Hopf technique: an alternative to the singular eigenfunction method. Advances in Nuclear Sci. Technology 7, 283–327, 1973.

    Google Scholar 

  25. A.C.Zaanen: Integration. Amsterdam, North-Holland Publ.Cie., 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The research for this article was done while the author was supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van der Mee, C.V.M. Spectral analysis of the Transport Equation. I. Nondegenerate and multigroup case. Integr equ oper theory 3, 529–573 (1980). https://doi.org/10.1007/BF01702315

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01702315

Keywords

Navigation