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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Transforms of measures on quotients and spline functions

Author: Alan MacLean
Journal: Trans. Amer. Math. Soc. 261 (1980), 287-296
MSC: Primary 43A25; Secondary 41A05
MathSciNet review: 576876
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Abstract: Let G be a LCA group with closed subgroup H and let $ v\, \in \,M(G/H)$. A general procedure is established for constructing a large family of measures in $ M(G)$ whose Fourier transforms interpolate $ \hat v$. This method is used to extend a theorem of Shepp and Goldberg by showing that if $ v\, \in \,M([0,\,2\pi ))$, then each even order cardinal spline function which interpolates the sequence $ (\hat v(n))_{n\, = \, - \,\infty }^\infty $ Fourier transform of a bounded Borel measure on R.

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Keywords: LCA group, bounded Borel measure, Fourier-Stieltjes transform, spline function
Article copyright: © Copyright 1980 American Mathematical Society