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Nonlinear maps in spaces of distributions

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References

  1. Ambrose, W.: Product of distributions with values in distributions. J. Reine Angew. Math.315, 525–533 (1980)

    MathSciNet  Google Scholar 

  2. Biagioni, H.A.: A nonlinear theory of generalized functions. (Lect. Notes Math., vol. 1421) Berlin Heidelberg New York: Springer 1990

    Book  MATH  Google Scholar 

  3. Colombeau, J.-F.: Introduction to new generalized functions, North-Holland (Math. Studies, vol. 113) Amsterdam: North Holland 1985

    Google Scholar 

  4. Colombeau, J.-F.: Multiplication of distributions. Bull. Am. Math. Soc., New Series23, 251–268 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Colombeau, J.-F., Oberguggenberger, M.: On a hyperbolic system with a compatible quadratic term: Generalized solutions, delta waves and multiplications. Commun. Partial Differ. Equations15, 905–938 (1990)

    MATH  MathSciNet  Google Scholar 

  6. Egorov, Y.: On the theory of generalized functions. Usp. Mat. Nauk,45:5, 1–40 (1990)

    MATH  Google Scholar 

  7. Hörmander, L.: The analysis of linear partial differential operators, vol. I–IV. Berlin Heidelberg New York: Springer 1983-85

    Google Scholar 

  8. Jelinek, J.: Characterization of the Colombeau product of distributions. Comment. Math. Univ. Carol.27, 337–394 (1986)

    MathSciNet  Google Scholar 

  9. Kadlubowska, E., Wawak, R.: Local order functions and regularity of the product of distributions. Bull. Pol. Acad. Sci. Math.32, 525–533 (1984)

    MathSciNet  Google Scholar 

  10. Komatsu, H.: Ultradistributions-I; structure theorems and a characterization. J. Fac. Sci., Univ. Tokyo, Sect. IA20, 25–105 (1974)

    MathSciNet  Google Scholar 

  11. Lysik, G.: On the regularity of the product of distributions Bull. Pol. Acad. Sci. Math.35, 203–210 (1987)

    MATH  MathSciNet  Google Scholar 

  12. Oberguggenberger, M.: Weak limits of solutions to semilinear hyperbolic systems. Math. Ann.274, 599–607 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Oberguggenberger, M.: Generalized solutions to semilinear hyperbolic systems. Monatsh. Math.103, 133–144 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  14. Pilipovic, S.: Tempered ultradistributions. Boll. Union Mat. Ital., VII Ser.,2-B, 235–251 (1988)

    MathSciNet  Google Scholar 

  15. Rauch, J., Reed, M.: Nonlinear superposition and absorption of delta waves in one space dimension. J. Funct. Anal.73, 152–178 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Rosinger, E.E.: Generalized solutions of nonlinear partial differential equations. (Math. Studies, vol. 147), Amsterdam: North Holland 1987

    MATH  Google Scholar 

  17. Schwartz, L.: Sur l'impossibilité de la multiplication des distributions. C.R. Acad. Sci. Paris, Ser. I239, 847–848 (1954)

    MATH  Google Scholar 

  18. Titchmarsh, E.C.: The theory of functions. Oxford: Oxford University Press 1939

    MATH  Google Scholar 

  19. Todorov, T.D.: Colombeau's generalized functions and non-standard analysis In: Stankovic, B., Pap, E., Pilipovic, S., Vladimirov, V. (eds.) Generalized functions, convergence structures and their applications. Proceedings, Dubrovnik 1987 (pp. 108–121) New York: Plenum press 1988

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Institute, Bulgarian Academy of Sciences, Department of Differential Equations, G. Bonchev Bl. 8, 1113, Sofia, Bulgaria

    T. Gramchev

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  1. T. Gramchev
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This research was started while the author was visiting University of Pisa, University of Ferrara and I.C.T.P., Trieste in the autumn of 1988

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Gramchev, T. Nonlinear maps in spaces of distributions. Math Z 209, 101–114 (1992). https://doi.org/10.1007/BF02570824

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  • DOI: https://doi.org/10.1007/BF02570824

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