Compactness in $L^ 2$ and the Fourier transform
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- by Robert L. Pego
- Proc. Amer. Math. Soc. 95 (1985), 252-254
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801333-9
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Abstract:
The Riesz-Tamarkin compactness theorem in ${L^p}({{\mathbf {R}}^n})$ employs notions of ${L^p}$-equicontinuity and uniform ${L^p}$-decay at $\infty$. When $1 \leqslant p \leqslant 2$, we show that these notions correspond under the Fourier transform, and establish new necessary and sufficient criteria for compactness in ${L^2}({{\mathbf {R}}^n})$.References
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Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 252-254
- MSC: Primary 42A38; Secondary 43A15
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801333-9
- MathSciNet review: 801333