Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function (Journal of Partial Differential Equations, 2000)
In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1}!.
Keywords: Heisenberg's inequality; ambiguity function; logarithmic Heisenberg's inequality; entropy