Skip to main content
SpringerLink
Log in

Associative and commutative distribution algebra with multipliers, and generalized solutions of nonlinear equations

  • Published:
Mathematical Notes Aims and scope Submit manuscript

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

References

  1. N. N. Bogolyubov and D. V. Shirokov,Introduction to Quantum Field Theory [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  2. E. Rosinger, “Nonsymmetric Dirac distributions in scattering theory,”Lect. Notes Math.,564, 391–399 (1976).

    MATH  MathSciNet  Google Scholar 

  3. V. P. Maslov and G. A. Omel'yanov, “Asymptotic soliton-type solutions of equations with small dispersion,”Usp. Mat. Nauk,36, No. 3, 63–126 (1981).

    MathSciNet  Google Scholar 

  4. V. P. Maslov and G. A. Omel'yanov, “On Hugoniot type conditions for infinitely narrow solutions of equations of simple waves,”Sib. Mat. Zh.,24, No. 5, 172–182 (1983).

    MathSciNet  Google Scholar 

  5. J. F. Colombeau,Elementary Introduction to New Generalized Functions, North Holland (1985).

  6. J. F. Colombeau and A. Y. Le Roux, “Multiplications of distributions in elasticity and hydrodynamics,”J. Math. Phys.,29, No. 2, 315–319 (1988).

    MathSciNet  Google Scholar 

  7. V. S. Vladimirov,Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  8. V. K. Ivanov, “On the multiplication for distributions of slow growth,”Izv. Vuzov Ser. Mat., No. 3, 10–19 (1972).

    MATH  Google Scholar 

  9. Yu. V. Egorov, “On the generalized function theory,”Usp. Mat. Nauk,45, No. 5, 3–40 (1990).

    MATH  Google Scholar 

  10. Ya. B. Livchak, “On the generalized function theory,” in:Tr. Rizhsk. Alg. Sem., Riga (1969), pp. 98–164.

  11. Li Bang-He, “Non-standard analysis and multiplication of distributions,”Acta Scientia Sinica,21, No. 5, 561–585 (1978).

    Google Scholar 

  12. V. K. Ivanov, “Asymptotic approximation to the product of generalized functions,”Izv. Vuzov Ser. Mat., No. 1, 19–26 (1981).

    MATH  Google Scholar 

  13. C. E. Francis, “Application of non-standard analysis to relativistic quantum mechanics,”J. Phys. A: Math. Gen.,14, 2539–2551 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  14. V. M. Shelkovich, “Distribution algebra with point singular support,”Dokl. Akad. Nauk SSSR,267, No. 1, 53–57 (1982).

    MATH  MathSciNet  Google Scholar 

  15. V. M. Shelkovich, “An associative distribution and multiplier algebra,”Dokl. Akad. Nauk SSSR,314, No. 1, 159–164 (1990).

    MATH  MathSciNet  Google Scholar 

  16. V. M. Shelkovich and A. P. Yuzhakov, “The structure of a class of Ivanov asymptotic distributions,”Izv. Vuzov Ser. Mat., No. 4, 70–73 (1991).

    MathSciNet  Google Scholar 

  17. T. A. Verzhbalovich,Some Questions Concerning the Theory of Multiplication of Generalized Functions of One or Several Variables, Sverdlovsk (1975).

  18. I. M. Gel'fand and G. E. Shilov,Generalized Functions and Operations upon Them [in Russian], Gos. Izd. Fiz. Mat. Lit., Moscow (1959).

    Google Scholar 

  19. R. Edwards,Functional Analysis [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  20. Yu. A. Bychkov, “On asymptotic expansions of generalized functions,”Mat. Zametki,12, No. 2, 131–138 (1972).

    MathSciNet  Google Scholar 

  21. G. Riordan,Combinatorial Identities [Russian translation], Nauka, Moscow (1982).

    Google Scholar 

  22. Yu. M. Shirokov, “A one-dimensional generalized function algebra,”Teor. Mat. Fiz.,39, No. 3, 291–301 (1979).

    MATH  MathSciNet  Google Scholar 

  23. G. Bierken and S. D. Drell,Relativistic Quantum Theory [Russian translation], Vol. 1, Nauka, Moscow (1978).

    Google Scholar 

  24. V. S. Vladimirov, “Problem of linear conjunction of holomorphic functions of many complex variables,”Izv. Akad. Nauk SSSR, Ser. Mat.,29, No. 4, 807–834 (1965).

    MATH  MathSciNet  Google Scholar 

  25. V. A. Kakichev and V. M. Shelkovich, “Solving boundary-value problems of the theory of analytic functions of many variables in Vladimirov algebras,”Mat. Zametki,22, No. 1, 51–60 (1977).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg University of Architecture and Civil Engineering, USSR

    V. M. Shelkovich

Authors
  1. V. M. Shelkovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 57, No. 5, pp. 765–783, May, 1995.

The author is grateful to G. A. Omelianov for discussions of questions related to generalized solutions of nonlinear equations.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelkovich, V.M. Associative and commutative distribution algebra with multipliers, and generalized solutions of nonlinear equations. Math Notes 57, 536–549 (1995). https://doi.org/10.1007/BF02304423

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02304423

Keywords

Search

Navigation