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

[21] Summability of Lagrange type interpolation series
Madych, WR
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2001, 84 (1): : 207 - 229
[22] Medina L.A., 2009, Scientia A: Math. Sci, P45
[23] The use of Sinc-collocation method for solving Falkner-Skan boundary-layer equation
Parand, K.
Dehghan, Mehdi
Pirkhedri, A.
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2012, 68 (01) : 36 - 47
[24] VARIATIONS ON BINOMIAL SERIES
POLLARD, H
SHISHA, O
[J]. AMERICAN MATHEMATICAL MONTHLY, 1972, 79 (05) : 495 - &
[25] A SINC FUNCTION ANALOGUE OF CHEBFUN
Richardson, Mark
Trefethen, Lloyd N.
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2011, 33 (05) : 2519 - 2535
[26] On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian
Schlumprecht, Th.
Sivakumar, N.
[J]. JOURNAL OF APPROXIMATION THEORY, 2009, 159 (01) : 128 - 153
[27] SCHOENBERG IJ, 1975, J ANAL MATH, V27, P205
[28] SPLINE FUNCTIONS .3. CONVERGENCE OF INTERPOLATING CARDINAL SPLINES AS THEIR DEGREE TENDS TO INFINITY
SCHOENBERG, IJ
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1973, 16 (01) : 87 - 93
[29] Titchmarsh E. C., 1939, THEORY FUNCTIONS
[30] SAMPLING BANDLIMITED FUNCTIONS OF POLYNOMIAL-GROWTH
WALTER, GG
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1988, 19 (05) : 1198 - 1203

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