Proceedings of the American Mathematical Society

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



Approximation of multipliers

Authors: Garth I. Gaudry and Ian R. Inglis
Journal: Proc. Amer. Math. Soc. 44 (1974), 381-384
MSC: Primary 43A22
MathSciNet review: 0340970
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Abstract: We note some necessary and sufficient conditions concerning norm approximation of Fourier multipliers, and give an example to show that $ {M_q}(Z)$, the space of Fourier multipliers of type $ (q,q)$, is not norm dense in $ {M_p}(Z)$ when $ 1 \leqq q < p \leqq 2$. An extension of this example to more general groups is indicated.

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Keywords: Locally compact abelian group, multiplier, approximation
Article copyright: © Copyright 1974 American Mathematical Society