Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces

被引：122

作者：

Aldroubi, A ^{[1
]}

Gröchenig, K ^{[1
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2000年 / 6卷 / 01期

关键词：

irregular sampling; spline; shift invariant spaces. frames; Wiener amalgam spaces; reproducing Kernel Hilbert spaces;

D O I：

10.1007/BF02510120

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under the appropriate definition of sampling density D-phi, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if D-phi greater than or equal to 1. This result is similar to Landau's result for the Paley-Wiener space B-1/2. If the shift invariant space consists of polynomial splines, then we show that D-phi < 1 is sufficient for the stable reconstruction of a function f from its samples, a result similar to Beurling's special case B-1/2.

引用

页码：93 / 103

页数：11

共 32 条

[1] SAMPLING PROCEDURES IN FUNCTION-SPACES AND SYMPTOTIC EQUIVALENCE WITH SHANNON SAMPLING THEORY [J].