A Sufficient Condition for the Uniform Convergence of Truncated Cardinal Functions Whittaker Inside the Interval

Authors

  • Alexandr Trynin

sinc approximation, interpolation functions, uniform approximation, cardinal functions Whittaker

Abstract

In terms of the one-sided module of continuity and positive (negative) module of change obtain sufficient conditions for the uniform convergence of truncated cardinal functions Whittaker inside the interval.

Downloads

How to Cite

A Sufficient Condition for the Uniform Convergence of Truncated Cardinal Functions Whittaker Inside the Interval. (2017). Global Journal of Science Frontier Research, 17(F7), 11-25. https://journalofscience.org/index.php/GJSFR/article/view/2091

References

Frank Stenger (1993) Sinc-Related Methods. 20, 243-310.

Livne Oren, E Brandt Achi, E (2011) MuST: The multilevel sinc transform. 33(4), 1726-1738.

L Coroianu, G Sorin (2016) Gal results for the non-truncated max-product sampling operators based on Fejer and sinc-type kernels. 49(1), 38-49.

Mark Richardson, Lloyd Trefethen (2011) A Sinc Function Analogue of Chebfun. 33(5), 2519-2535.

M Khosrow, R Yaser, S Hamed (2016) Numerical Solution for First Kind Fredholm Integral Equations by Using Sinc Collocation Method. 6(3), 120-128.

M Marwa (2014) Tharwat Sinc approximation of eigenvalues of Sturm-Liouville problems with a Gaussian multiplier Calcolo: a quarterly on numerical analysis and theory of computation. 51, 465-484.

M Alquran, K Al-Khaled (2011) Numerical Comparison of Methods for Solving Systems of Conservation Laws of Mixed Type. 5(1), 35-47.

J Chen, E Lu, B Huang (2007) Sampling theorem for multiwavelet subspaces. 11.

Ingrid Daubechies (1992) Ten Lectures on Wavelets.

I Novikov, S Stechkin (1997) Basic wavelet theory. 53(6), 1159-1231.

I Maksimenko, M Skopina (2004) Multivariate periodic wavelets. 15(2), 165-190.

J Brown (1967) On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem. 18(1), 75-84.

P Butzer, J Higgins, R Stens (2005) Classical and approximate sampling theorems; studies in the http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll">LP(R) and the uniform norm. 137(2), 250-263.

A Shmukler, T Shulman (1974) Certain properties of Kotel'nikov series. 66(7), 93-103.

V Sklyarov (2008) On the best uniform sinc-approximation on a finite interval. 14(2), 183-192.

(2014) New Perspectives on Approximation and Sampling Theory, Applied and Numerical Harmonic Analysis.

Andi Kivinukk, Gert Tamberg (2009) Interpolating Generalized Shannon Sampling Operators, Their Norms and Approximation Properties. 8(1), 77-95.

A Trynin, V Sklyarov (2008) Error of Sine Approximation of Analytic Functions on an Interval. 7(3), 263-270.

Trynin Yu (2007) Estimates for the Lebesgue functions and the Nevai formula for the sinc approximations of continuous functions on an interval. 48(5), 929-938.

Trynin Yu (2007) Tests for pointwise and uniform convergence of sinc approximations of continuous functions on a closed interval. 198(10), 1517-1534.

Trynin Yu (2008) A criterion for the uniform convergence of sinc-approximations on a segment. 52(6), 58-69.

Trynin Yu (2010) On divergence of sinc-approximations everywhere on (0, π). 22(4), 683-701.

Trynin Yu (2009) A generalization of the Whittaker-Kotel'nikov-Shannon sampling theorem for continuous functions on a closed interval. 200(11), 1633-1679.

Trynin Yu (2000) On the absence of stability of interpolation in eigenfunctions of the Sturm-Liouville problem. 44(9), 58-71.

Trynin Yu (2010) The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm-Liouville problem. 54(11), 66-76.

Trynin Yu (2011) On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange-Jacobi polynomials. 75(6), 1215-1248.

Trynin Yu (2015) On some properties of sinc approximations of continuous functions on the interval. 7(4), 111-126.

Trynin Yu (2015) On necessary and sufficient conditions for convergence of sinc approximations. 27(5), 170-194.

Trynin Yu (2016) Approximation of continuous on a segment functions with the help of linear combinations of sincs. 60(3), 63-71.

Trynin Yu (2013) On inverse nodal problem for Sturm-Liouville operator. 5(4), 112-124.

Trynin Yu (2011) Differential properties of zeros of eigen functions of the Sturm-Liouville problem. 3(4), 133-143.

K Mochizuki, I Trooshin (2011) On the Scattering on a Loop-shaped Graph. 227-245.

A Privalov (1986) Uniform convergence of lagrange interpolation processes. 39(2), 124-133.

Z Chanturiya (1976) On uniform convergence of Fourier series. 29(4), 475-495.

M Dyachenko (2013) On a class of summability methods for multiple Fourier series. 204(3), 307-322.

S Volosivets, B Golubov (2015) Uniform convergence and integrability of multiplicative Fourier transforms. 98(1-2), 53-67.

Farkov Yu (2014) On the best linear approximation of holomorphic functions. 19(5), 185-212.

D Borisov, S Dmitriev (2017) On the Spectral Stability of Kinks in 2D Klein-Gordon Model with Parity‐Time‐Symmetric Perturbation. 138(3), 317-342.

Denis Borisov, Giuseppe Cardone, Tiziana Durante (2016) Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. 146(6), 1115-1158.

Pokornyi Yu, M Zvereva, S Shabrov (2008) Sturm-Liouville oscillation theory for impulsive problems. 63(1), 109-153.

A Sufficient Condition for the Uniform Convergence of Truncated Cardinal Functions Whittaker Inside the Interval

Published

2017-11-20

How to Cite

A Sufficient Condition for the Uniform Convergence of Truncated Cardinal Functions Whittaker Inside the Interval. (2017). Global Journal of Science Frontier Research, 17(F7), 11-25. https://journalofscience.org/index.php/GJSFR/article/view/2091