Convergence of Classical Cardinal Series and Band Limited Special Functions

被引：6

作者：

Bailey, B. A. ^{[1
]}

Madych, W. R. ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2013年 / 19卷 / 06期

关键词：

Cardinal series; Symmetric partial sums; Entire functions of exponential type; Special band limited functions; Sampling theorems; Asymptotic growth bounds; SAMPLING THEOREM; INTERPOLATION; RECOVERY; SPLINES; SPACES;

D O I：

10.1007/s00041-013-9291-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the behavior of symmetric partial sums of the classical cardinal series. Necessary and sufficient conditions for convergence are recorded and a bound on the asymptotic behavior of the limiting function is established. Questions concerning sampling, uniqueness, and the effect of index shifts are also addressed. Examples of certain band limited special functions that can be expressed as limits of symmetric partial sums of classical cardinal series are included.

引用

页码：1207 / 1228

页数：22

共 36 条

[1] Abramowitz M., 1966, HDB MATH FUNCTIONS F
[2] [Anonymous], STUDIES ADV MATH
[3] Boas Jr R., 1972, TOHOKU MATH J, V24, P121, DOI DOI 10.2748/TMJ/1178241524
[4] Behavior of Shannon's Sampling Series for Hardy Spaces
Boche, Holger
Moenich, Ullrich J.
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2009, 15 (03) : 404 - 412
[5] BROWM JL, 1968, J MATH ANAL APPL, V21, P699
[6] ON ERROR IN RECONSTRUCTING A NON-BANDLIMITED FUNCTION BY MEANS OF BANDPASS SAMPLING THEOREM
BROWN, JL
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1967, 18 (01) : 75 - &
[7] Classical and approximate sampling theorems;: studies in the LP (R) and the uniform norm
Butzer, PL
Higgins, JR
Stens, RL
[J]. JOURNAL OF APPROXIMATION THEORY, 2005, 137 (02) : 250 - 263
[8] Butzer PL, 2000, DEVELOPMENT OF MATHEMATICS 1950-2000, P193
[9] Coroianu L., 2011, Sampl. Theory Signal Image Process., V10, P211
[10] Davis PJ, 1975, INTERPOLATION APPROX

← 1 2 3 4 →