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?
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Cf. this – J. W. Tanner Jun 29 '21 at 01:21
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@J.W.Tanner I was Hardy's uncertainty principle! (I remember now: the book was Hörmander's) Thank you. – SolutionExists Jun 29 '21 at 01:26
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Heisenberg uncertainty principle in $d$ dimensions says that $$\frac{|xf(x)|_2}{|f(x)|_2}\frac{|\xi\hat{f}(\xi)|_2}{|\hat{f}(x)|_2}\ge\frac{d}{4\pi}$$ – robjohn Jun 29 '21 at 05:17
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Yes, there is Hardy's uncertainty principle in harmonic analysis.
J. W. Tanner
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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. – Mark S. Jun 29 '21 at 13:25