Entropy versus influence for complex functions of modulus one

09/27/2020

∙

by   Gideon Schechtman, et al.

∙

0

∙

share

We present an example of a function f from {-1,1}^n to the unit sphere in ℂ with influence bounded by 1 and entropy of |f̂|^2 larger than 1/2log n. We also present an example of a function f from {-1,1}^n to ℝ with L_2 norm 1, L_∞ norm bounded by √(2), influence bounded by 1 and entropy of f̂^2 larger than 1/2log n.