Skip to main content
SpringerLink
Log in

Transport theory inL p-spaces

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

Abstract

In this article boundary value problems of linear transport theory are studied inL p-spaces (1≤p<+∞). It is shown that the results valid inL 2-space can also be derived inL p-space (1≤p<+∞). For a non-multiplying medium formal expressions for the solutions are obtained.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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. J. Bognár: Indefinite inner product spaces. Heidelberg, Springer Verlag, 1974.

    Google Scholar 

  3. S. Chandrasekhar: Radiative transfer. Second revised edition. New York, Dover Publ., 1960.

    Google Scholar 

  4. J.J. Duderstadt, W.R. Martin: Transport theory. A Wiley -Interscience Publication, John Wiley & Sons, 1979.

  5. N. Dunford, J.T. Schwarz: Linear operators. I. New York, Interscience, 1958.

    Google Scholar 

  6. I.A. Feldman: Wiener-Hopf operator equations and their application to the transport equation. Integral equations and operator theory 3, 43 - 61, 1980 = Matem. Issled. 6 (3), 115 –132, 1971 (Russian).

    Google Scholar 

  7. I.A. Feldman: On some projection methods for the solution of the equation of radiative energy transfer. Matem. Issled. 7 (4), 228 - 236, 1972 (Russian).

    Google Scholar 

  8. I.C. Gohberg, G. Heinig: On matrix integral equations on finite intervals with kernels depending on the difference of their arguments. Rev. Roum. Math. Pures et Appl. 20, 55 - 73, 1975 (Russian).

    Google Scholar 

  9. I.C. Gohberg, M.G. Krein: Systems of integral equations on a half-line with kernels depending of the difference of arguments. A.M.S. Transl. 14, 217 -287, 1960 = Uspehi Matem. Nauk 13 (2), 3 – 72, 1959 (Russian).

    Google Scholar 

  10. 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 

  11. 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 

  12. I.C. Gohberg, E.I. Sigal: An operator generalization of the logarithmic residue theorem and the theorem of Rouché. Math. USSR Sbornik 13, 603 - 625, 1971 = Mat. Sbornik 84 (126), 607 - 629, 1971 (Russian).

    Google Scholar 

  13. W. Greenberg, P.F. Zweifel: Functional-analytic treatment of the transport equation. Transport Theory and Statistical Physics 5, 219 - 253, 1976.

    Google Scholar 

  14. R.J. Hangelbroek: Linear analysis and solution of neutron transport problems. Transport Theory and Statistical Physics 5, 1 - 85, 1976.

    Google Scholar 

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

    Google Scholar 

  16. H.C. van de Hulst: Multiple light scattering: tables, formulas and applications. I, II. New York, Academic Press, 1980.

    Google Scholar 

  17. T. Kato: Perturbation theory for linear operators. Heidelberg, Springer Verlag, 1966.

    Google Scholar 

  18. E.W. Larsen: Solutions of neutron transport problems inL 1. Comm. on Pure and Appl. Math. 28, 729 - 746, 1975.

    Google Scholar 

  19. E.W. Larsen: S. Sancaktar, P.F. Zweifel: Extension of the Case formulas toL p. Application to half- and full-space problems. J. Math. Phys. 16, 1117 - 1121, 1975.

    Google Scholar 

  20. C.G. Lekkerkerker: The linear transport equation. The degenerate case c = 1. I. Full-range theory; II. Half-range theory. Proc. Royal Soc. Edinburgh 75 A, 259 - 282 & 283 – 295, 1975.

    Google Scholar 

  21. M.V. Maslennikov: The Milne problem with anisotropic scattering. Proc. of the Steklov institute of mathematics, vol. 97, 1968 = Trudy matem. instituta im. V.A. Steklova, AN SSSR, 97, 1968 (Russian).

  22. C.V.M. van der Mee: Semigroup and factorization methods in Transport Theory. Amsterdam, Mathematical Centre Tract 146, 1981.

  23. V.V. Sobolev: Light scattering in planetary atmospheres. Oxford, Pergamon Press, 1975.

    Google Scholar 

  24. K. Stummel: Discrete convergence of linear operators, II. Math. Zeitschrift 120, 231 - 264, 1971 (German).

    Google Scholar 

  25. A.E. Taylor: Introduction to functional analysis. New York, John Wiley & Sons, 1964.

    Google Scholar 

  26. V.S. Vladimirov: Mathematical problems of the one-speed particle transprt theory. Trudy matem. instituta im. V.A. Steklova, AN SSSR, 61, 1961 (Russian).

  27. A.C. Zaanen: Integration. Amsterdam, North-Holland, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wiskundig Seminarium (= Dept. of Mathematics), Vrije Universiteit, Amsterdam, The Netherlands

    C. V. M. van der Mee

Authors
  1. C. V. M. van der Mee
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

van der Mee, C.V.M. Transport theory inL p-spaces. Integr equ oper theory 6, 405–443 (1983). https://doi.org/10.1007/BF01691906

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01691906

Keywords

Search

Navigation