Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines

被引：0

作者：

Groechenig, Karlheinz ^{[1
]}

Shafkulovska, Irina ^{[1
]}

机构：

[1] Univ Vienna, Fac Math, Oskar-Morgenstern-Platt 1, A-1090 Vienna, Austria

来源：

JOURNAL OF APPROXIMATION THEORY | 2025年 / 306卷

基金：

奥地利科学基金会;

关键词：

Shift-invariant spaces; Splines; Chebyshev B-splines; Collocation matrix; Schoenberg-Whitney condition; Nonuniform sampling; Gabor frames; GABOR FRAMES; RECONSTRUCTION; APPROXIMATION; DENSITY; INTERPOLATION;

D O I：

10.1016/j.jat.2024.106118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive samples. These conditions are near optimal, and, in particular, they imply the existence of sampling sets with lower Beurling density arbitrarily close to the necessary density. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：37

共 34 条

[1] Compressive Hermite Interpolation: Sparse, High-Dimensional Approximation from Gradient-Augmented Measurements [J].

Adcock, Ben ;

Sui, Yi .

CONSTRUCTIVE APPROXIMATION, 2019, 50 (01) :167-207

[2] Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements [J].

Adcock, Ben ;

Gataric, Milana ;

Hansen, Anders C. .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2017, 23 (06) :1311-1347

[3] Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces:: The Lp-theory [J].

Aldroubi, A ;

Feichtinger, H .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (09) :2677-2686

[4] Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces [J].

Aldroubi, A ;

Gröchenig, K .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2000, 6 (01) :93-103

[5] Nonuniform sampling and reconstruction in shift-invariant spaces [J].

Aldroubi, A ;

Gröchenig, K .

SIAM REVIEW, 2001, 43 (04) :585-620

[6] Discretized Gabor Frames of Totally Positive Functions [J].

Bannert, Severin ;

Groechenig, Karlheinz ;

Stoeckler, Joachim .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (01) :159-169

[7] TRANSLATES OF EXPONENTIAL BOX SPLINES AND THEIR RELATED SPACES [J].

BENARTZI, A ;

RON, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 309 (02) :683-710

[8]

Benedetto J.J., 2001, Applied and Numerical Harmonic Analysis

[9]

Benedetto John J., 1995, J FOURIER ANAL APPL, V1, P355, DOI 10.1007/ s00041- 001- 4016- 5

[10]

Carleson Lennart, 1989, Complex Analysis. Volume 2: Harmonic Analysis, V1

← 1 2 3 4 →