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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

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References

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

    Google Scholar 

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

    Google Scholar 

  3. N. Bleistein and J. K. Cohen, “Nonuniqueness in the inverse source problem in acoustics and electromagnetics,” J. Math. Phys.,18, No. 2, 194–201 (1977).

    Article  Google Scholar 

  4. A. S. Zapreev and V. A. Tsetsokho, “Some inverse problems of oscillation theory,” Zh. Vychisl. Matematiki i Mat. Fiziki,23, No. 5, 1158–1167 (1983).

    Google Scholar 

  5. V. R. Kireitov, “The Cauchy problem in the whole space and a certain inverse problem for the equations of propagation of mean spatial illumination,” Dokl. Akad. Nauk SSSR,284, No. 5, 1066–1069 (1985).

    Google Scholar 

  6. V. R. Kireitov, “The Dirichlet problem for the equationδ 1/2 u=f in a domain with regular compact boundary,” Dokl. Akad. Nauk SSSR,321, No. 5, 896–899 (1991).

    Google Scholar 

  7. J. Deny, “Noyaux de convolution de Hunt et noyaux associés à une famille fondamentale,” Ann. Inst. Fourier (Grenoble),12, 643–667 (1962).

    Google Scholar 

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

    Google Scholar 

  9. A. Beurling and J. Deny, “Dirichlet spaces,” Proc. Nat. Acad. Sci. U.S.A.,45, 208–215 (1959).

    Google Scholar 

  10. F. Hirsch, “Intégrales de résolvantes et calcul symbolique,” Ann. Inst. Fourier (Grenoble),22, No. 4, 239–264 (1972).

    Google Scholar 

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

    Google Scholar 

  12. M. ItÔ, “Sur le principle de domination pour les noyaux de convolution,” Nagoya Math. J.,50, 149–174 (1973).

    Google Scholar 

  13. M. ItÔ, “Characterizations of supports of balayaged measures,” Nagoya Math. J.,28, 203–230 (1966).

    Google Scholar 

  14. M. Ohtsuka, “On potentials in locally compact spaces,” J. Sci. Hiroshima Univ.,25, No. 2, 135–352 (1961).

    Google Scholar 

  15. K. Kunugui, “étude sur la théorie du potential généralisé,” Osaka Math. J.,2, 63–103 (1950).

    Google Scholar 

  16. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals [Russian translation], Gostekh-izdat, Moscow-Leningrad (1948).

    Google Scholar 

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Authors and Affiliations

  1. Novosibirsk

    V. R. Kireitov

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  1. V. R. Kireitov
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Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 3, pp. 551–572, May–June, 1995.

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Kireitov, V.R. 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. Sib Math J 36, 472–490 (1995). https://doi.org/10.1007/BF02109836

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  • DOI: https://doi.org/10.1007/BF02109836

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