Approximation of multipliers
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- by Garth I. Gaudry and Ian R. Inglis PDF
- Proc. Amer. Math. Soc. 44 (1974), 381-384 Request permission
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.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- R. E. Edwards, Fourier series: A modern introduction. Vol. I, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1967. MR 0216227
- R. E. Edwards, Uniform approximation on noncompact spaces, Trans. Amer. Math. Soc. 122 (1966), 249–276. MR 196472, DOI 10.1090/S0002-9947-1966-0196472-5
- Alessandro Figà-Talamanca, Translation invariant operators in $L^{p}$, Duke Math. J. 32 (1965), 495–501. MR 181869
- Alessandro Figà-Talamanca and Garth I. Gaudry, Multipliers of $L^{p}$ which vanish at infinity, J. Functional Analysis 7 (1971), 475–486. MR 0276689, DOI 10.1016/0022-1236(71)90029-2
- Donald E. Ramirez, Uniform approximation by Fourier-Stieltjes transforms, Proc. Cambridge Philos. Soc. 64 (1968), 323–333. MR 221221, DOI 10.1017/s0305004100042882
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 381-384
- MSC: Primary 43A22
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340970-8
- MathSciNet review: 0340970