A characterization of absolute continuity by means of Mellin integral operators (Q496883)
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scientific article; zbMATH DE number 6484446
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| English | A characterization of absolute continuity by means of Mellin integral operators |
scientific article; zbMATH DE number 6484446 |
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A characterization of absolute continuity by means of Mellin integral operators (English)
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22 September 2015
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Summary: In the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical \(\mathrm{BV}\)-spaces, both in the one-dimensional and in the multidimensional setting.
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Mellin integral operators
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absolute continuity
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multidimensional variation
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convergence in variation
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