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On the norm continuity of the hk-fourier transform

This work is partially supported by CONACyT-SNI and VIEP-BUAP (Puebla, Mexico)

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  • In this work we study the Cosine Transform operator and the Sine Transform operator in the setting of Henstock-Kurzweil integration theory. We show that these related transformation operators have a very different behavior in the context of Henstock-Kurzweil functions. In fact, while one of them is a bounded operator, the other one is not. This is a generalization of a result of E. Liflyand in the setting of Lebesgue integration.

    Mathematics Subject Classification: Primary: 26A39, 43A32; Secondary: 26A42, 26A45.


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