## A class of extremal functions for the Fourier transform

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- by S. W. Graham and Jeffrey D. Vaaler
- Trans. Amer. Math. Soc.
**265**(1981), 283-302 - DOI: https://doi.org/10.1090/S0002-9947-1981-0607121-1
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## Abstract:

We determine a class of real valued, integrable functions $f(x)$ and corresponding functions ${M_f}(x)$ such that $f(x) \leqslant {M_f}(x)$ for all $x$, the Fourier transform ${\hat M_f}(t)$ is zero when $\left | t \right | \geqslant 1$, and the value of ${\hat M_f}(0)$ is minimized. Several applications of these functions to number theory and analysis are given.## References

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## Bibliographic Information

- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**265**(1981), 283-302 - MSC: Primary 42A38; Secondary 10H30
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607121-1
- MathSciNet review: 607121