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.References
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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