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Algebra i Analiz, 2007, Volume 19, Issue 4, Pages 113–138 (Mi aa130)  

Research Papers

A uniqueness theorem for Riesz potentials

K. A. Izyurov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: The existence is proved of a nonzero Hölder function $f\colon\mathbb{R}\to\mathbb{R}$ that vanishes together with its M. Riesz potential $f\ast\frac{1}{|x|^{1-\alpha}}$ at all points of some set of positive length. This result improves that of D. Beliaev and V. Havin.

Keywords: Riesz potential, uncertainty principle, Hölder condition.

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English version:
St. Petersburg Mathematical Journal, 2008, 19:4, 577–595

Bibliographic databases:

MSC: 31A15, 31A20
Received: 08.02.2007

Citation: K. A. Izyurov, “A uniqueness theorem for Riesz potentials”, Algebra i Analiz, 19:4 (2007), 113–138; St. Petersburg Math. J., 19:4 (2008), 577–595

Citation in format AMSBIB
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\paper A~uniqueness theorem for Riesz potentials
\jour Algebra i Analiz
\yr 2007
\vol 19
\issue 4
\pages 113--138
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2381935}
\zmath{https://zbmath.org/?q=an:1207.31002}
\transl
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 4
\pages 577--595
\crossref{https://doi.org/10.1090/S1061-0022-08-01011-X}
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