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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convolution equations in certain Banach spaces
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by Alexander L. Koldobskii PDF
Proc. Amer. Math. Soc. 111 (1991), 755-765 Request permission

Abstract:

For a Banach space $E$ and $p > 0$, the following problem is considered: how to identify a finite Borel measure $\mu$ on $E$ by means of the potential $g(a) = \int _E {||x - a|{|^p}d\mu (x),a \in E}$. The solution for infinite-dimensional Hilbert spaces is based on limit correlations between the Fourier transforms of finite-dimensional restrictions of $g$ and $||x|{|^p}$. For finite-dimensional subspaces of ${L_p}$, the Levy representation of norms is used.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 111 (1991), 755-765
  • MSC: Primary 46F25; Secondary 46G12, 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1034886-1
  • MathSciNet review: 1034886