Multiplication of distributions

Volker Boie

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 309-321
  • ISSN: 0010-2628

Abstract

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Multiplication by harmonic representations of distributions, introduced by Li Banghe, is an extension of a certain product by radial (rotationally symmetric) mollifiers and therefore a strict extension of the Kami'{n}ski and Colombeau product.

How to cite

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Boie, Volker. "Multiplication of distributions." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 309-321. <http://eudml.org/doc/248224>.

@article{Boie1998,
abstract = {Multiplication by harmonic representations of distributions, introduced by Li Banghe, is an extension of a certain product by radial (rotationally symmetric) mollifiers and therefore a strict extension of the Kami'\{n\}ski and Colombeau product.},
author = {Boie, Volker},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {distribution products; multiplication; harmonic representations; Kami'nski product; distribution products; multiplication; harmonic representations; Kamiński product},
language = {eng},
number = {2},
pages = {309-321},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Multiplication of distributions},
url = {http://eudml.org/doc/248224},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Boie, Volker
TI - Multiplication of distributions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 309
EP - 321
AB - Multiplication by harmonic representations of distributions, introduced by Li Banghe, is an extension of a certain product by radial (rotationally symmetric) mollifiers and therefore a strict extension of the Kami'{n}ski and Colombeau product.
LA - eng
KW - distribution products; multiplication; harmonic representations; Kami'nski product; distribution products; multiplication; harmonic representations; Kamiński product
UR - http://eudml.org/doc/248224
ER -

References

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  1. Boie V., Partielle Multiplikationen in Distributionenräumen, Dissertation, Universität Hannover, 1996. Zbl0876.46032
  2. Itano M., On the multiplicative product of distributions, J. Sci. Hiroshima Univ., Ser. A-I 29 (1965), 51-74. (1965) MR0184079
  3. Jelínek J., Distinguishing example for the Tillmann product of distributions, Comment. Math. Univ. Carolinae 31 (1990), 693-700. (1990) MR1091366
  4. Jelínek J., A contribution to the equivalence results for the product of distributions, Comment. Math. Univ. Carolinae 35 (1994), 263-266. (1994) MR1286573
  5. Jelínek J., Characterization of the Colombeau product of distributions, Comment. Math. Univ. Carolinae 27 (1986), 377-394. (1986) MR0857556
  6. Kamiński A., Convolution, product and Fourier transform of distributions, Studia Math. 74 (1982), 83-96. (1982) MR0675434
  7. Langebruch M., Randverteilungen von Nullösungen hypoelliptischer Differentialgleichungen, Manuscripta Math. 26 (1978), 17-35. (1978) MR0513144
  8. Li Banghe, Nonstandard analysis and multiplication of distributions, Scientia Scinica, Ser. A 21 (1978), 561-585. (1978) MR0513744
  9. Li Banghe, Li Yaqing, Nonstandard analysis and multiplication of distributions in any dimension, Scientia Scinica, Ser. A 28 (1985), 716-726. (1985) Zbl0597.46034MR0813857
  10. Li Banghe, Li Yaqing, On the harmonic and analytic representations of distributions, Scientia Scinica, Ser. A 28 (1985), 923-937. (1985) Zbl0597.46039
  11. Liu Shangping, Distributions in 𝒟 ' ( ℝ n ) as boundary values of harmonic functions, Scientia Scinica, Ser. A 27 (1984), 897-904. (1984) MR0767622
  12. Oberguggenberger M., Products of distributions: Nonstandard methods, Zeitschr. Anal. Anw. 7 (1988), 347-365; Correction: {Zeitschr. Anal. Anw.} 10 (1991), 263-264. (1988) Zbl0662.46048MR0963445
  13. Oberguggenberger M., Multiplication of distributions and applications to partial differential equations, Pitman Research Notes in Mathematics, vol. 259, 1992. Zbl0818.46036MR1187755
  14. Schwartz L., Sur l'impossibilité de la multiplication des distributions, C.R. Acad. Sci., Paris 239 (1954), 847-848. (1954) Zbl0056.10602MR0064324
  15. Schwartz L., Théorie des distributions, Hermann, Paris, nouv. edition, 1966. Zbl0962.46025MR0209834
  16. Tillmann H.G., Darstellung der Schwartzschen Distributionen durch analytische Funktionen, Math. Zeitschr. 77 (1961), 106-124. (1961) Zbl0099.09703MR0139002
  17. Wawak R., On the Colombeau product of distributions, in Generalized functions and convergence, P. Antosik and A. Kamiński, eds., World Scientific, Singapore, 1990, pp.279-284. MR1085515

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