Journal of Science of the Hiroshima University, Series A-I (Mathematics)

On the theory of the multiplicative products of distributions

Mitsuyuki Itano

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math., Volume 30, Number 2 (1966), 151-181.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206139107

Digital Object Identifier
doi:10.32917/hmj/1206139107

Mathematical Reviews number (MathSciNet)
MR0209835

Zentralblatt MATH identifier
0145.38502

Subjects
Primary: 46.40

Citation

Itano, Mitsuyuki. On the theory of the multiplicative products of distributions. J. Sci. Hiroshima Univ. Ser. A-I Math. 30 (1966), no. 2, 151--181. doi:10.32917/hmj/1206139107. https://projecteuclid.org/euclid.hmj/1206139107


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References

  • [1] H. J. Bremermann, On finite renormalization constants and the multiplication of causal functions in perturbation theory, Technical Report, Department of Mathematics, University of California, Berkeley, July 1962.
  • [2] and L. Durand, On analytic continuation, multiplication, and Fourier transformations of Schwartz distributions, J. Math. Physics, 2 (1961), 240-258.
  • [3] V. V. Grusin, Fundamental solutions of hypoelliptic equations, Uspehi Mat. Nauk, 16 (1961), 147-153 (in Russian).
  • [4] Y. Hirata and H. Ogata, On the exchange formula for distributions, this Journal, 22 (1958), 147-152.
  • [5] L. Hormander, Linear partial differential operators, Springer, (1963).
  • [6] M. Itano, On the multiplicative products of distributions, this Journal, 29 (1965), 51-74.
  • [7] E. M. de Jager, Divergent convolution integrals in electrodynamics, Technical Report, Department of Mathematics, University of California, Berkeley, August 1963.
  • [8] J. Jelinek, Sur le produit simple de deux distributions, Comment. Math. Univ. Carolinae, 5 (1964), 209- 214.
  • [9] H. Knig, Multiplikation von Distributionen I, Math. Ann., 128 (1955), 420-452.
  • [10] H. Knig, Multiplikationstheorie der verallgemeinerten Distributionen, Bayer Akad. Wiss. Math. -Nat.Kl. Abh. (N.F.), 82 (1957).
  • [11] S. Lojasiewicz, Sur la valeur et la limite d'une distribution en un point, Studia Math., 16 (1957). 1-36.
  • [12] S. Lojasiewicz, Sur la fixation des variables dans une distribution, Studia Math., 17 (1958), 1-64.
  • [13] J. Mikusiski, Criteria of the existence and of the associativity of the product of distributions, Studia Math., 21 (1962), 253-259.
  • [14] L. Schwartz, Sur impossibilit de la multiplication des distributions, C. R. Acad. Sci. Paris, 239 (1954), 847-848.
  • [15] L. Schwartz, Theorie des distributions, I, II, Paris, Hermann (1951).
  • [16] L. Schwartz, Theorie des distributions a valeurs vectorielles, Chap. I, Ann. Inst. Fourier, 7 (1957), 1-141.
  • [17] R. Shiraishi, On -convolutions of vector valued distributions, this Journal, 27 (1963), 173-212.
  • [18] and M. Itano, On the multiplicative products of distributions, this Journal, 28 (1964), 223- 235.
  • [19] H. G. Tillmann, Darstellung der Schwartzschen Distributionen durch analytische Funktionen, Math. Z., 77 (1961), 106-124.