# The product of a function and a Boehmian

Colloquium Mathematicae (1993)

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

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topNemzer, 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

top- [1] N. K. Bary, A Treatise on Trigonometric Series, Pergamon Press, New York, 1964. Zbl0129.28002
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- [3] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983. Zbl0521.35001
- [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] J. Mikusiński, Operational Calculus, Pergamon Press, Oxford, 1959. Zbl0088.33002
- [6] P. Mikusiński, Convergence of Boehmians, Japan. J. Math. 9 (1983), 159-179. Zbl0524.44005
- [7] P. Mikusiński, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281. Zbl0652.44005
- [8] P. Mikusiński, On harmonic Boehmians, Proc. Amer. Math. Soc. 106 (1989), 447-449.
- [9] D. Nemzer, Periodic Boehmians II, Bull. Austral. Math. Soc. 44 (1991), 271-278. Zbl0744.46022
- [10] D. Nemzer, The Laplace transform on a class of Boehmians, ibid. 46 (1992), 347-352.
- [11] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966.
- [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] 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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