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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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 ${L^2}({{\mathbf {R}}^n})$.
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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