This article is cited in 4 papers

Short Communications

On recovery of a measure from its symmetrization

A. A. Gushchin^a, U. Küchler<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b Humboldt University, Department of Mathematics

Abstract: We show that a $\sigma$-finite Borel measure, which is defined on the positive half-line and has a nonincreasing density (with respect to the Lebesgue measure) is uniquely characterized by its symmetrization.

Keywords: symmetrization, phase retrieval, Fourier transform, factorization theorems, moving average process.

Received: 28.01.2004

DOI: 10.4213/tvp224

 English version: Theory of Probability and its Applications, 2005, 49:2, 323–333

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