Geodesic
Absolute convergence of multiple Fourier integrals
Yurii Kolomoitsev1 ; Elijah Liflyand2
1Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Rosa Luxemburg St. 74 Donetsk 83114, Ukraine
2Department of Mathematics Bar-Ilan University 52900 Ramat-Gan, Israel
Studia Mathematica, Tome 214 (2013) no. 1, pp. 17-35
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of $L_p$ integrability of the function and its partial derivatives, each with a different $p$. These $p$ are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
DOI : 10.4064/sm214-1-2
Keywords: various sufficient conditions representation function several variables absolutely convergent fourier integral obtained results given terms integrability function its partial derivatives each different these subject certain relations known earlier only particular cases sharpness applications results obtained discussed

Yurii Kolomoitsev  1   ; Elijah Liflyand  2

1 Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Rosa Luxemburg St. 74 Donetsk 83114, Ukraine
2 Department of Mathematics Bar-Ilan University 52900 Ramat-Gan, Israel 
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Yurii Kolomoitsev; Elijah Liflyand. Absolute convergence of multiple Fourier integrals. Studia Mathematica, Tome 214 (2013) no. 1, pp. 17-35. doi: 10.4064/sm214-1-2

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