The product of a function and a Boehmian

Dennis Nemzer

Colloquium Mathematicae (1993)

  • Volume: 66, Issue: 1, page 49-55
  • ISSN: 0010-1354

Abstract

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Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

How to cite

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Nemzer, Dennis. "The product of a function and a Boehmian." Colloquium Mathematicae 66.1 (1993): 49-55. <http://eudml.org/doc/210233>.

@article{Nemzer1993,
abstract = {Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.},
author = {Nemzer, Dennis},
journal = {Colloquium Mathematicae},
keywords = {generalized functions; Boehmians; convergence structure; product},
language = {eng},
number = {1},
pages = {49-55},
title = {The product of a function and a Boehmian},
url = {http://eudml.org/doc/210233},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Nemzer, Dennis
TI - The product of a function and a Boehmian
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 1
SP - 49
EP - 55
AB - Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.
LA - eng
KW - generalized functions; Boehmians; convergence structure; product
UR - http://eudml.org/doc/210233
ER -

References

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  1. [1] N. K. Bary, A Treatise on Trigonometric Series, Pergamon Press, New York, 1964. Zbl0129.28002
  2. [2] I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. 2, Academic Press, New York, 1968. 
  3. [3] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983. Zbl0521.35001
  4. [4] L. L. Littlejohn and R. P. Kanwal, Distributional solutions of the hypergeometric differential equation, J. Math. Anal. Appl. 122 (1987), 325-345. Zbl0629.34006
  5. [5] J. Mikusiński, Operational Calculus, Pergamon Press, Oxford, 1959. Zbl0088.33002
  6. [6] P. Mikusiński, Convergence of Boehmians, Japan. J. Math. 9 (1983), 159-179. Zbl0524.44005
  7. [7] P. Mikusiński, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281. Zbl0652.44005
  8. [8] P. Mikusiński, On harmonic Boehmians, Proc. Amer. Math. Soc. 106 (1989), 447-449. 
  9. [9] D. Nemzer, Periodic Boehmians II, Bull. Austral. Math. Soc. 44 (1991), 271-278. Zbl0744.46022
  10. [10] D. Nemzer, The Laplace transform on a class of Boehmians, ibid. 46 (1992), 347-352. 
  11. [11] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. 
  12. [12] S. M. Shah and J. Wiener, Distributional and entire solutions of ordinary differential and functional differential equations, Internat. J. Math. and Math. Sci. 6 (1983), 243-270. Zbl0532.34006
  13. [13] J. Wiener, Generalized-function solutions of differential and functional differential equations, J. Math. Anal. Appl. 88 (1982), 170-182. Zbl0489.34080

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