论文标题
小波变换的Donoho-logan大筛原理
Donoho-Logan large sieve principles for the wavelet transform
论文作者
论文摘要
在本文中，我们为小波在强大的空间上的小波转换制定了Donoho和Logan的大筛原理，将最大奈奎斯特密度的概念转化为基础空间的双曲线几何形状。结果为$ L_ {1} $ - 最小化方法提供了确定性的保证，并保留一类母小波，这些小波构成了Hardy空间的正常基础，并且可以与较高的双曲线Landau水平相关联。基础函数的明确计算揭示了与Zernike多项式的联系。我们证明了一个新颖的局部再现公式，用于考虑空间，并使用它来得出相应小波变换的大筛型浓度估计。最后，我们根据尼古拉和蒂利的开创性方法基于库利科夫，拉莫斯和蒂利的最新结果来讨论分析案例中定位的最佳性。这导致了小波变换的急剧不确定性原理和局部利用不平等。
In this paper we formulate Donoho and Logan's large sieve principle for the wavelet transform on the Hardy space, adapting the concept of maximum Nyquist density to the hyperbolic geometry of the underlying space. The results provide deterministic guarantees for $L_{1}$-minimization methods and hold for a class of mother wavelets which constitute an orthonormal basis of the Hardy space and can be associated with higher hyperbolic Landau levels. Explicit calculations of the basis functions reveal a connection with the Zernike polynomials. We prove a novel local reproducing formula for the spaces in consideration and use it to derive concentration estimates of the large sieve type for the corresponding wavelet transforms. We conclude with a discussion of optimality of localization in the analytic case by building on recent results of Kulikov, Ramos and Tilli based on the groundbreaking methods of Nicola and Tilli. This leads to a sharp uncertainty principle and a local Lieb inequality for the wavelet transform.
