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The Walsh–Fourier Transform on the Real Line

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Abstract

The element of the Walsh system, that is the Walsh functions map from the unit interval to the set \(\{-1,1\}\). They can be extended to the set of nonnegative reals, but not to the whole real line. The aim of this article is to give a Walsh-like orthonormal and complete function system which can be extended on the real line.

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ACKNOWLEDGMENTS

The first author is indebted to Professor Kaoru Yoneda and wishes to thank for a personal conversation happened around 2003 and the idea of ‘‘going left,’’ ‘‘stay,’’ or ‘‘going right’’.

Funding

The first author is supported by projects EFOP-3.6.2-16-2017-00015 and EFOP-3.6.1-16-2016-00022 supported by the European Union, cofinanced by the European Social Fund. The second author is very thankful to United Arab Emirates University (UAEU) for the Start-up Grant 12S100.

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Authors and Affiliations

  1. University of Debrecen, Debrecen, Hungary

    G. Gát

  2. United Arab Emirates University, Abu Dhabi, Al Ain, UAE

    U. Goginava

Authors
  1. G. Gát
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  2. U. Goginava
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Corresponding authors

Correspondence to G. Gát or U. Goginava.

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The authors declare that they have no conflicts of interest.

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Gát, G., Goginava, U. The Walsh–Fourier Transform on the Real Line. J. Contemp. Mathemat. Anal. 57, 205–214 (2022). https://doi.org/10.3103/S1068362322040057

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  • DOI: https://doi.org/10.3103/S1068362322040057

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