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An Interplay of Multidimensional Variations in Fourier Analysis
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.
Keywords:
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