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Proceedings of the American Mathematical Society

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

 

 

Quadratic forms in harmonic analysis and the Bochner-Eberlein theorem


Author: Roger A. Horn
Journal: Proc. Amer. Math. Soc. 52 (1975), 263-270
MSC: Primary 43A35; Secondary 60E05
MathSciNet review: 0374823
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Abstract: New characterizations are given of the classes of functions on a locally compact Abelian group which are Fourier-Stieltjes transforms of: bounded measures, nonnegative bounded measures, and integrable functions. These characterizations are all of the same form, viz., that a positive definite Hermitian form dominate a symmetric quadratic form.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374823-7
Keywords: Fourier-Stieltjes transforms, positive definite functions, Bochner's theorem, Eberlein's theorem
Article copyright: © Copyright 1975 American Mathematical Society