On basicity of exponentials inLP (dμ) and general prediction problems
On basicity of exponentials inLP (dμ) and general prediction problems
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关于 LP (dμ) 指数的基本性和一般预测问题
DOI：
10.1007/bf01876313
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发表时间：
1993
影响因子：
0.8
通讯作者：
A. Miamee
中科院分区：
文献类型：
--
作者：
A. Miamee
设μ是复平面上单位圆上的一个非负测度，且1<p<∞。我们感兴趣的是找到μ上的条件，使幂指数θ的集合形成lp （dμ）的强基。本文证明了部分结果，对这一重要的开放性问题提供了一些启示。这些结果在随机过程预测理论和其他领域的应用中具有重要的基础意义。然后利用这些结果得到一个定理，该定理将一些预测问题简化为更简单的预测问题。
Let μ be a nonnegative measure on the unit circle in the complex plane and 1<p<∞. It is of interest to find conditions on μ so that the set of exponentialseinθ form a strongM-basis forLp(dμ). Some partial results are proved which can shed some light on this important open question. These results are of fundamental importance in the prediction theory of stochastic processes and other fields of applications. These results is then used to obtain a theorem which reduces some prediction problems to easier ones.