Let f be a differentiable complex valued function on R. If f is square integrable, then it is not the case that f(x) must approach zero at infinity. counterexample: f(x)=x^2 exp(-x^8 sin^2(20x)).(adsbygoogle = window.adsbygoogle || []).push({});

If I also require that the derivative of f be square integrable, is that enough to guarantee that lim x-> +/- infinity of f(x) is zero?

Thanks,

KH

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Square integrable/vanish at infinity?

Loading...

Similar Threads - Square integrable vanish | Date |
---|---|

I Integral involving square and log | Apr 9, 2017 |

I Integrating x-squared | Dec 15, 2016 |

Fourier, square sign wave, f(x)sin(kx) integration | Nov 27, 2015 |

Squaring Integrals | Sep 12, 2015 |

Integral of exponential over square root | Jul 5, 2015 |

**Physics Forums - The Fusion of Science and Community**