TY - JOUR
T1 - Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function
AU - Guji Tian 
JO - Journal of Partial Differential Equations
VL - 3
SP - 207
EP - 216
PY - 2000
DA - 2000/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5507.html
KW - Heisenberg's inequality
KW - ambiguity function
KW - logarithmic Heisenberg's inequality
KW - entropy
AB -  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}!.