An Interplay of Multidimensional Variations in Fourier Analysis

E. Liflyand; U. Stadtmüller; R. Trigub

doi:10.1007/s00041-010-9136-3

An Interplay of Multidimensional Variations in Fourier Analysis

E. Liflyand
, U. Stadtmüller
, R. Trigub

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	226-239
Number of pages	14
Journal	Journal of Fourier Analysis and Applications
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00041-010-9136-3
State	Published - Apr 2011

Keywords

Bounded variation
Fourier integral
Trigonometric series

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10.1007/s00041-010-9136-3

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title = "An Interplay of Multidimensional Variations in Fourier Analysis",

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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author = "E. Liflyand and U. Stadtm{\"u}ller and R. Trigub",

year = "2011",

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AU - Liflyand, E.

AU - Stadtmüller, U.

AU - Trigub, R.

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N2 - 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.

AB - 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.

KW - Bounded variation

KW - Fourier integral

KW - Trigonometric series

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JO - Journal of Fourier Analysis and Applications

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An Interplay of Multidimensional Variations in Fourier Analysis

Abstract

Keywords

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