Nonuniform Sampling and Recovery of聽Multidimensional Bandlimited Functions by聽Gaussian Radial-Basis Functions

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• 作者：B. A. Bailey (1) abailey@math.tamu.edu
  T. Schlumprecht (1) schlump@math.tamu.edu
  N. Sivakumar (1) sivan@math.tamu.edu
• 关键词：Scattered data – ; Gaussian interpolation – ; Multidimensional bandlimited functions
• 刊名：Journal of Fourier Analysis and Applications
• 出版时间：June 2011
• 出版年：2011
• 期刊代码：77_1069-5869
• 类别：mat
• 卷：17
• 期：3
• 页码：519-533
• 数据来源：sp

摘要

Let S⊂ℝ d be a bounded subset with positive Lebesgue measure. The Paley-Wiener space associated to S, PW _S , is defined to be the set of all square-integrable functions on ℝ d whose Fourier transforms vanish outside S. A sequence (x _j :j∈ℕ) in ℝ d is said to be a Riesz-basis sequence for L ₂(S) (equivalently, a complete interpolating sequence for PW _S ) if the sequence (e-i谩x_j,·帽:j 脦 \mathbb N)(e^{-i\langle x_{j},\cdot \rangle }:j\in \mathbb {N}) of exponential functions forms a Riesz basis for L ₂(S). Let (x _j :j∈ℕ) be a Riesz-basis sequence for L ₂(S). Given λ>0 and f∈PW _S , there is a unique sequence (a _j ) in ℓ ₂ such that the function I_l(f)(x):=氓_{j 脦 \mathbb N}a_je-l||x-x_j||₂2, x 脦 \mathbb Rd,I_\lambda(f)(x):=\sum_{j\in \mathbb {N}}a_je^{-\lambda \|x-x_j\|_2^2},\quad x\in \mathbb {R}^d,