Growth properties of Hartley transform via moduli of continuity

Kakharman N. Tokmagambetov N.
December 2024 Birkhauser

Journal of Pseudo-Differential Operators and Applications
2024 #15 Issue 4

This study investigates the relationship between the moduli of continuity of a function and its Hartley transform. We explore this connection by deriving significant results such as the Riemann–Lebesgue lemma, Parseval’s theorem, and the Hausdorff–Young inequality for the Hartley transform in both the Euclidean space and torus. Using a translation operator, we obtain an analog of Titchmarsh’s theorem for the Hartley transform. In addition, we extend our analysis to the Hartley series on the torus.

43A32 , 44A30 , Hartley transform , Hausdorff–Young inequality , Modulus of smoothness , Riemann–Lebesgue Lemma , Titchmarsh’s theorem

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Institute of Mathematics and Mathematical Modeling, 28 Shevchenko str., Almaty, 050010, Kazakhstan
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Cerdanyola del Vallés (Barcelona), 08193, Spain

Institute of Mathematics and Mathematical Modeling
Centre de Recerca Matemática

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