$L^2(R^d)$中的标准正交序列与时频局部化
Orthonormal sequences in $L^2(R^d)$ and time frequency localization
摘要：
研究了$L^2(\R^d)$中规范正交基和序列的测不准原理。在经典的海森堡不等式中，我们关注的是一个函数的色散和它的傅里叶变换的乘积。特别是，我们证明了没有规范正交基的$L^2(\R)$的时间和频率的手段，以及产品的分散体是一致有界的。这个问题与J.Benedetto，A. Powell和Ph. Jaming。我们的主要工具是$L^2(\R^d)$中正交序列的时频局部化不等式。它还有其他各种用途。
英文摘要：
We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.
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