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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



A uniqueness theorem for Riesz potentials

Author: K. A. Izyurov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 4.
Journal: St. Petersburg Math. J. 19 (2008), 577-595
MSC (2000): Primary 31A15, 31A20
Published electronically: May 9, 2008
MathSciNet review: 2381935
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Abstract | References | Similar Articles | Additional Information

Abstract: The existence is proved of a nonzero Hölder function $f:\mathbb {R}\rightarrow \mathbb {R}$ 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.

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Additional Information

K. A. Izyurov
Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, Universitetskii Prospekt 28, Staryi Peterhof, St. Petersburg 198504, Russia

Keywords: Riesz potential, uncertainty principle, Hölder condition
Received by editor(s): February 8, 2007
Published electronically: May 9, 2008
Additional Notes: Partially supported by RFBR (grant no. 06-01-00313).
Article copyright: © Copyright 2008 American Mathematical Society