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Projection-iteration method of solution of the equations of quantum field theory and its connection with the theory of renormalization. The equations of quantum field theory and improperly posed problems of mathematical physics

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Literature Cited

  1. R. Jost, The General Theory of Quantized Fields, AMS, Providence, R.I. (1965).

    Google Scholar 

  2. Constructive Field Theory [collection of papers translated from the English], Mir (1977).

  3. S. S. Ivanov, D. Ya. Petrina, and A. L. Rebenko, Fiz. Elem. Chastits At. Yadra,7, 647 (1976).

    Google Scholar 

  4. G. V. Efimov, Nonlocal Interactions of Quantized Fields [in Russian], Nauka (1977).

  5. N. N. Bogolyubov and O. S. Parasyuk, Izv. Akad. Nauk SSSR, Ser. Mat.,20, 585 (1956).

    Google Scholar 

  6. N. N. Bogolyubov and O. S. Parasiuk, Acta. Math.,97, 227 (1957).

    Google Scholar 

  7. O. S. Parasyuk, Izv. Akad. Nauk SSSR, Ser. Mat.,20, 843 (1956).

    Google Scholar 

  8. K. Hepp, Commun. Math. Phys.,6, 161 (1967).

    Google Scholar 

  9. S. A. Anikin, O. I. Zav'yalov, and M. K. Polivanov, Teor. Mat. Fiz.,17, 189 (1973).

    Google Scholar 

  10. S. A. Anikin and M. K. Polivanov, Teor. Mat. Fiz.,21, 175 (1974).

    Google Scholar 

  11. V. A. Shcherbina, Doct. Diss., MI AN SSSR (1975).

  12. W. Zimmermann, Commun. Math. Phys.,6, 161 (1967).

    Google Scholar 

  13. O. I. Zav'yalov, Teor. Mat. Fiz.,28, 27 (1976).

    Google Scholar 

  14. V. A. Shcherbina, Teor. Mat. Fiz.,14, 342 (1973).

    Google Scholar 

  15. R. P. Feynman, Phys. Rev.,74, 939 (1948).

    Google Scholar 

  16. F. T. Dyson, Phys. Rev., 1436 (1949).

  17. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Improperly Posed Problems [in Russian], Nauka (1974).

  18. V. K. Ivanov, Dokl. Akad. Nauk SSSR,145, 270 (1962).

    Google Scholar 

  19. S. S. Ivanov, D. Ya. Petrina, and A. L. Rebenko, Teor. Mat. Fiz.,19, 37 (1974).

    Google Scholar 

  20. D. Ya. Petrina and A. L. Rebenko, Preprint ITP-78-165E, Kiev (1979).

  21. N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, Interscience (1959).

  22. D. Ya. Petrina, Teor. Mat. Fiz.,4, 389 (1970).

    Google Scholar 

  23. S. S. Ivanov, D. Ya. Petrina, and A. L. Rebenko, Teor. Mat. Fiz.,23, 160 (1975).

    Google Scholar 

  24. A. L. Rebenko, Preprint ITP-74-41E, Kiev (1974).

  25. T. Hadamard, Le Probleme Cauchy, Paris (1932).

  26. A. N. Tikhonov, Dokl. Akad. Nauk SSSR,39, 195 (1943).

    Google Scholar 

  27. N. S. Kurpel, Projection-Iteration Methods of Solution of Operator Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  28. V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Improperly Posed Problems and Applications [in Russian], Nauka (1978).

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Authors
  1. D. Ya. Petrina
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  2. A. L. Rebenko
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Additional information

Institute of Theoretical Physics, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 42, No. 2, pp. 167–183, February, 1980.

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Petrina, D.Y., Rebenko, A.L. Projection-iteration method of solution of the equations of quantum field theory and its connection with the theory of renormalization. The equations of quantum field theory and improperly posed problems of mathematical physics. Theor Math Phys 42, 110–120 (1980). https://doi.org/10.1007/BF01032112

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  • DOI: https://doi.org/10.1007/BF01032112

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