For the Fourier transform of the convolution in and D' and Z'

Authors

  • Vasko Rechkoski Faculty of Tourism and Hospitality, University St. Kliment Ohridski, Bitola, Republic of North Macedonia.
  • Bedrije Bedzeti Faculty of Mathematics and Natural Sciences, State University of Tetovo, Tetovo, Republic of North Macedonia.
  • Vesna Manova Erakovikj Faculty of Mathematics and Natural Sciences, Ss. Cyril and Methodius University, Skopje, Republic of North Macedonia.

DOI:

https://doi.org/10.24297/jam.v20i.8927

Keywords:

Space Z', space D', inverse Fourier trensform, Fourier transforms, convolution of distributions

Abstract

In this paper, we give another proof of the known lemma considering the Fourier transform of the convolution of a distribution and a function. Also, we give its application in the mentioned spaces.

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References

H. Bremerman: Raspredelenija, kompleksnijepermenenije i preobrazovanija Furje, Izdatelstvo ‘’Mir’’, Moskva, 1968.

Beltrami, E.J. and M.R. Wohlers: Distributions and the boundary values of analytic functions, Academic Press, New York, 1966. https://doi.org/10.1016/B978-1-4832-3168-6.50006-4

R. Carmichael, D. Mitrovic: Distributions and analytic functions, New York, 1989.

Jantcher: Distributionen, Walter de Gruyter, Berlin, New York, 1971.

N. Reckoski: One proof for the analytic representation of distributions, Matematicki Bilten 28 (LIV), Skopje, 2004 (19-30).

W. Rudin: Real and Complex Analysis, McGraw-Hill Inc., New York, 1966.

W. Rudin: Functional Analysis, North-Holland publishing company, Amsterdam, 1974.

A.H. Zemanian: Distribution Theory and Transform Analysis, McGraw-Hill Company, New York, 1965.

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Published

2021-01-06

How to Cite

Rechkoski, V., Bedzeti, B., & Erakovikj, V. M. (2021). For the Fourier transform of the convolution in and D’ and Z’ . JOURNAL OF ADVANCES IN MATHEMATICS, 20, 1–7. https://doi.org/10.24297/jam.v20i.8927

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Articles