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Convolution equations in certain Banach spaces


Author: Alexander L. Koldobskii
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
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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 {\vert\vert x - a\vert{\vert^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 $ \vert\vert x\vert{\vert^p}$. For finite-dimensional subspaces of $ {L_p}$, the Levy representation of norms is used.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1034886-1
Article copyright: © Copyright 1991 American Mathematical Society

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