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The stationary translation-invariant peierls equation of the theory of radiation transport in the space of tempered distributions and some properties of the Peierls potential. I

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References

  1. V. R. Kireîtov, “The Cauchy problem, the Dirichlet problem, and some inverse problems for the one-velocity Peierls equation of the theory of radiation transport in a homogeneously absorbing and scattering medium with isotropic sources,” Sibirsk. Mat. Zh.,36, No. 3, 551–572 (1995).

    Google Scholar 

  2. V. R. Kireîtov, “The Cauchy problem, the Dirichlet problem, and some inverse problem for the one-velocity Peierls equation of the theory of radiation transport in a homogeneously absorbing and scattering medium with isotropic sources,” Dokl. Akad. Nauk,262, No. 2, 176–179 (1995).

    Google Scholar 

  3. V. R. Kireîtov, “The Dirichlet problem for the equation Δ1/2 u = ƒ in a domain with a compact regular boundary,” Dokl. Akad. Nauk SSSR,321, No. 5, 896–899 (1991).

    Google Scholar 

  4. B. Davison, Neutron Transport Theory [Russian translation], Atomizdat, Moscow (1960).

    Google Scholar 

  5. V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  6. N. S. Landkof, Fundamentals of Modern Potential Theory [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  7. K. Yosida, “Positive resolvents and potentials,” Z. Wahrscheinlichkeitstheorie Verw. Geb, No. 8, 210–218 (1967).

    Article  MATH  Google Scholar 

  8. J. Deny, “Sur les espaces de Dirichlet,” Sém. de Theorie du Potentiel. 1 Annee. Fac. des Sci. Paris,1, No. 5, 1–14 (1957).

    Google Scholar 

  9. S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  10. T. Ugaheri, “On the potential and capacity,” Japan J. Math.,20, 37–43.

  11. M. Ohtsuka, “On potentials in locally compact spaces,” J. Sci. Hiroshima Univ. Ser. A1 Math.,25, 135–352 (1961).

    MATH  Google Scholar 

  12. K. Kunugui, “Étude sur la theorie du potentiel généralisé,” Osaka J. Math.,2, 63–103 (1950).

    MATH  Google Scholar 

  13. N. Ninomyia, “Sur le principle du maximum et le balayage,” Japan J. Math.,29, 68–77 (1959).

    Google Scholar 

  14. N. Ninomyia, “’Etude sur la théorie du potentiel pris rapport au noyau symétrique,” J. Inst. Polytech. Osaka City Univ. Ser. A,8, 147–179 (1957).

    Google Scholar 

  15. M. Kishi, “Maximum principles in the potential theory,” Nagoya Math. J.,23, 165–187 (1963).

    MATH  Google Scholar 

  16. I. Higuchi and M. Ito, “On the theorem of Kishi for a continuous function-kernel,” Nagoya Math. J.,53, 127–135 (1974).

    MATH  Google Scholar 

  17. J. Deny, “Les principes fondamentaux de la theorie du potentiel,” Sém. de Theorie du Potentiel dirige par M. Brelot, G. Choquet et J. Deny,5, No. 6, pp. 1–9 (1960/61).

    Google Scholar 

  18. G. A. Hunt, Markoff Processes and Potentials [Russian translation], Izdat. Inostr. Lit., Moscow (1962).

    MATH  Google Scholar 

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Authors
  1. V. R. Kireĭtov
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Novosibirks. Translated fromSibirskiî Matematicheskiî Zhhurnal, Vol. 38, No. 3, pp. 533–550, May–June, 1997.

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Kireĭtov, V.R. The stationary translation-invariant peierls equation of the theory of radiation transport in the space of tempered distributions and some properties of the Peierls potential. I. Sib Math J 38, 455–470 (1997). https://doi.org/10.1007/BF02683834

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