scholarly journals On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series

2019 ◽  
Vol 62 (4) ◽  
pp. 1163-1171 ◽  
Author(s):  
Keaton Hamm
Keyword(s):  
Generalized Sampling ◽  
Sampling Series ◽  
Interpolation Series ◽  
Cardinal Functions

AbstractWe investigate the Gibbs–Wilbraham phenomenon for generalized sampling series, and related interpolation series arising from cardinal functions. We prove the existence of the overshoot characteristic of the phenomenon for certain cardinal functions, and characterize the existence of an overshoot for sampling series.

Kantorovich-Type Generalized Sampling Series in the Setting of Orlicz Spaces

2007 ◽  
Vol 6 (1) ◽  
pp. 29-52 ◽  
Author(s):  
C. Bardaro ◽  
G. Vinti ◽  
P. L. Butzer ◽  
R. L. Stens
Keyword(s):  
Orlicz Spaces ◽  
Generalized Sampling ◽  
Sampling Series

On the Approximation by Generalized Sampling Series in Lp-Metrics

2006 ◽  
Vol 5 (1) ◽  
pp. 59-87
Author(s):  
Z. Burinska ◽  
K. Runovski ◽  
H.-J. Sehmeisser
Keyword(s):  
Generalized Sampling ◽  
Sampling Series

scholarly journals Approximation by pseudo-linear discrete operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
İsmail Aslan ◽  
Türkan Yeliz Gökçer
Keyword(s):  
Error Estimation ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Discrete Operator ◽  
Generalized Sampling ◽  
Sampling Series ◽  
Discrete Operators ◽  
Generator Function ◽  
Uniformly Continuous

<p style='text-indent:20px;'>In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.</p>

scholarly journals An Inverse Result of Approximation by Sampling Kantorovich Series

2018 ◽  
Vol 62 (1) ◽  
pp. 265-280 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Real Line ◽  
Representation Formula ◽  
Order Of Approximation ◽  
Generalized Sampling ◽  
Representation Formulas ◽  
Sampling Series ◽  
Bounded Functions ◽  
Saturation Theorem ◽  
Uniformly Continuous ◽  
Kantorovich Operators

AbstractIn the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

scholarly journals Approximation by sampling-type nonlinear discrete operators in φ-variation

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2731-2746
Author(s):  
İsmail Aslan
Keyword(s):  
Close Relationships ◽  
Nonlinear Approximation ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Lipschitz Classes ◽  
Generalized Sampling ◽  
Convergence In Variation ◽  
Sampling Series ◽  
Discrete Operators

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in ?-variation. Angeloni and Vinti prove some approximation results considering linear sampling-type discrete operators. These types of operators have close relationships with generalized sampling series. By improving Angeloni and Vinti?s one, we aim to get a nonlinear approximation which is also generalized by means of summability process. We also evaluate the rate of approximation under appropriate Lipschitz classes of ?-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our kernel assumptions.

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