Heisenberg inequalities for Jacobi transforms

作者：Ma Ruiqin^*

来源：Journal of Mathematical Analysis and Applications, 2007, 332(1): 155-163.

DOI：10.1016/j.jmaa.2006.09.044

• uncertainty principle
• Jacobi transform
• Jacobi-Dunkl transform

The classical Heisenberg uncertainty principle states that for f is an element of L-2(R),
integral(x2)(R)vertical bar f(x)vertical bar(2)dx . integral(R)xi(2)vertical bar(f) over cap(xi)vertical bar(2)d xi >= 1/4 vertical bar vertical bar f vertical bar vertical bar(4).
In this paper, we obtain this inequality and variants of it for the Jacobi transform. It implies an analogue for the Jacobi-Dunkl transform. The proof is based on ultracontractive properties of the semigroups generated by the Jacobi differential operator and on the estimate on the heat kernel.

• 出版日期2007-8-1
• 单位北京理工大学