Long time ago, I read in a math textbook a statement about functions of complex variables. It was a named uncertainty principle. The name attached was NOT Heisenberg. I know of Heisenberg's uncertainty principle. The one I read in that textbook was similar but seemed more fundamental. Are there any uncertainty principles in the theory of complex variables?

  • $\begingroup$ Cf. this $\endgroup$ Jun 29, 2021 at 1:21
  • $\begingroup$ @J.W.Tanner I was Hardy's uncertainty principle! (I remember now: the book was Hörmander's) Thank you. $\endgroup$ Jun 29, 2021 at 1:26
  • $\begingroup$ Heisenberg uncertainty principle in $d$ dimensions says that $$\frac{\|xf(x)\|_2}{\|f(x)\|_2}\frac{\|\xi\hat{f}(\xi)\|_2}{\|\hat{f}(x)\|_2}\ge\frac{d}{4\pi}$$ $\endgroup$
    – robjohn
    Jun 29, 2021 at 5:17

1 Answer 1


Yes, there is Hardy's uncertainty principle in harmonic analysis.

  • $\begingroup$ It's not easy to find Hardy's uncertainty principle in that page/via that top-level link. Terry Tao has a blog post mentioning Hardy's Uncertainty Principle and a weak form of it. $\endgroup$
    – Mark S.
    Jun 29, 2021 at 13:25

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