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An Interplay of Multidimensional Variations in Fourier Analysis |
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| Authors: | E Liflyand U Stadtm??ller R Trigub |
| Institution: | 1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel 2. Department of Mathematics, University of Ulm, 89069, Ulm, Germany 3. Department of Mathematics, Donetsk National University, 83055, Donetsk, Ukraine |
| Abstract: | We compare the Fourier integral of a function of bounded variation and the corresponding trigonometric series, generated by that function, in the multidimensional case. Several known notions of bounded variation are used and a new one is introduced. The obtained results are applied to integrability of multidimensional trigonometric series. |
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