平方可积函数

Periodic signals which are neither absolutely integrable nor square integrable over an infinite interval, can be considered to have Fourier transforms if impulse functions are permitted in the transform.

若在变换过程中可以使用冲激函数，那么，在一个无限区间内，既不绝对可积，又不具备平方可积的周期信号也可以认为具有傅立叶级数。

On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function.

本文基于雷达信号和雷达模糊度函数间的一致关系，提出了任意平方可积的二维有界函数是雷达模糊度函数的充要条件，并且指出它包括了Wilcox提出的离散的可实现条件。

We will prove that the only compact dual Toeplitz operator is the zero operator, and that a densely defined dual Toeplitz operator with square integrable symbol is bounded if and only if its symbol is essentially bounded.

首先，我们证明了只有零算子是紧的对偶Toeplitz算子，同时给出了以平方可积函数为符号稠定义的对偶Toeplitz算子有界当且仅当它的符号函数是本性有界的。

While in quantum mechanics the state of a system is described by a wave function, which is a non-zero square modulus integrable complex value function defined on the configuration space of the system.

整个世界的运动是决定论的。而在量子力学中每个体系的状态由一个非零的定义在位形空间上模平方可积的复值函数所描写。

It is proven that the radial wavelet family generated from a single radial wavelet can constitute a frame in L〓 and the square integrable function can be reconstructed from its dyadic radial wavelet transform.

得出这样的结论：由一个本质上为一维的径向小波的伸缩和平移可以构成n维平方可积函数空间L〓的框架。

We all know that mother wavelet function can create waveletframe, and the kernel function with wavelet frame can build a group of basis insquare integral space only by translation.

由于母小波函数可以生成小波框架，我们用小波框架来构造核函数，而采用该核函数的SVM，能够逼近平方可积空间中的任意函数。

However, to construct a tensor product orthonomal wavelet basis in L〓, 2〓-1 different functions are used. Furthermore, it is concluded that the family, obtained by dilations and translations from this radial wavelet as well as their linear combinations, can constitute an orthonomal basis in L〓. The conclusion is a major breakthrough in multidimensional wavelet analysis.

从而得到：由一个径向小波的伸缩、平移系及其线性组合可以构成n维平方可积函数空间L〓的规范正交基，这个结果将当前利用张量积方法构造n维正交小波基所需要的2〓-1个不同的函数降为仅需要一个径向小波函数，这在理论上是一个重大突破；构造了同时具备局部支撑和无穷次连续可微性质的高维不可分小波的例子，这是不同于I。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。