Sketch of Proof
The proof of this tight inequality depends on the so-called (q, p)-norm of the Fourier transformation. (Establishing this norm is the most difficult part of the proof.) From this norm we are able to establish a lower bound on the sum of the (differential) Rényi entropies where For simplicity, we consider this inequality only in one dimension; the extension to multiple dimensions is straightforward and can be found in the literature cited.
Read more about this topic: Entropic Uncertainty
Famous quotes containing the words sketch and/or proof:
“We criticize a man or a book most sharply when we sketch out their ideal.”
—Friedrich Nietzsche (1844–1900)
“It comes to pass oft that a terrible oath, with a swaggering accent sharply twanged off, gives manhood more approbation than ever proof itself would have earned him.”
—William Shakespeare (1564–1616)