再生核希尔伯特空间中的框架分析与逼近
Frame analysis and approximation in reproducing kernel Hilbert spaces
摘要：
我们考虑给定Hilbert空间中的框架F，证明了每个框架F都可以由周围希尔伯特空间中的再生核和规范正交基构造性地得到.构造是算子理论的，建立在从F定义的分析算子的几何公式上。我们的重点是在无限维的情况下，先验估计发挥了核心作用，我们延长了一些结果是已知的，到目前为止，只有在有限的尺寸。我们进一步展示了如何使用这种方法可以在分析和应用中构建有用的框架，并在理解它们的几何形状和对称性。
英文摘要：
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building on a geometric formula for the analysis operator defined from F. Our focus is on the infinite-dimensional case where a priori estimates play a central role, and we extend a number of results which are known so far only in finite dimensions. We further show how this approach may be used both in constructing useful frames in analysis and in applications, and in understanding their geometry and their symmetries.
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