Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function

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Volume 13, Issue 3

Guji Tian

J. Part. Diff. Eq., 13 (2000), pp. 207-216.

Published online: 2000-08

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Abstract

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

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@Article{JPDE-13-207, author = {Guji Tian }, title = {Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {207--216}, abstract = { 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}!.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5507.html} }

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}!.

Guji Tian . (2000). Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function. Journal of Partial Differential Equations. 13 (3). 207-216. doi:

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