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$ L\sp{p}$-convolution operators supported by subgroups


Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Proc. Amer. Math. Soc. 34 (1972), 475-478
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0296215-9
MathSciNet review: 0296215
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Abstract: Let G be a compact nonabelian group and H be a closed subgroup of G. Then H is a set of spectral synthesis for the Fourier algebra $ A(G)$ (and indeed for $ {A^p}(G),1 \leqq p < \infty $). For $ 1 \leqq p < \infty $, each $ {L^p}(G)$-multiplier T corresponds to a $ {L^p}(H)$-multiplier S by the rule $ (Tf)\vert H = S(f\vert H),f \in A(G)$, if and only if the support of T is contained in H.


References [Enhancements On Off] (What's this?)

  • [1] C. Dunkl and D. Ramirez, Topics in harmonic analysis, Appleton-Century-Crofts, New York, 1971. MR 0454515 (56:12766)
  • [2] A. Figà-Talamanca, Translation invariant operators in $ {L^p}$, Duke Math. J. 32 (1965), 495-501. MR 31 #6095. MR 0181869 (31:6095)
  • [3] C. Herz, Synthèse spectrale pour les sous-groupes par rapport aux algèbres $ {A_p}$, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A316-A318. MR 42 #8307b. MR 0273429 (42:8307b)
  • [4] -, Le rapport entre l'algèbre $ {A_p}$ d'un groupe et d'un sous-groupe, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A244-A246. MR 42 #8307a.
  • [5] S. Saeki, Translation invariant operators on groups, Tôhoku Math. J. 22 (1970), 409-419. MR 0275057 (43:815)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296215-9
Keywords: Fourier algebra, spectral synthesis, $ {L^p}$-multiplier
Article copyright: © Copyright 1972 American Mathematical Society

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