Sampling Type Operators Research Articles

Weighted approximations by sampling type operators: recent and new results

In this paper, we collect some recent results on the approximation properties of generalized sampling operators and Kantorovich operators, focusing on pointwise and uniform convergence, rate of convergence, and Voronovskaya-type theorems in weighted spaces of functions. In the second part of the paper, we introduce a new generalization of sampling Durrmeyer operators including a special function $\rho$ which satisfies certain assumptions. For the family of newly constructed operators, we obtain pointwise convergence, uniform convergence and rate of convergence for functions belonging to weighted spaces of functions.

Erratum: A unifying approach to convergence of linear sampling type operators in Orlicz spaces

Erratum for the article [1]: G. Vinti and L. Zampogni, A unifying approach to convergence of linear sampling type operators in Orlicz spaces, Advances in Differential Equations, 16 (2011), No. 5-6, 573-600.

Quantitative estimates for sampling type operators with respect to the Jordan variation

In this paper, we study the order of approximation with respect to the Jordan variation for the generalized and the Kantorovich sampling series, based upon averaged type kernels. In particular, we establish some quantitative estimates for the above operators. For the latter purpose, we introduce a suitable modulus of smoothness in the space of absolutely continuous functions on the whole real line.

Linear prediction and simultaneous approximation by m-th order Kantorovich type sampling series

In the present paper, a new family of sampling type operators is introduced and studied. By the composition of the well-known generalized sampling operators of P.L. Butzer with the usual differential and anti-differential operators of order m, we obtain the so-called m-th order Kantorovich type sampling series. This family of approximation operators are very general and include, as special cases, the well-known sampling Kantorovich and the finite-differences operators. Here, we discuss about pointwise and uniform convergence of the m-th order Kantorovich type sampling series; further, quantitative estimates for the order of approximation have been established together with asymptotic formulas and Voronovskaja type theorems. In the latter results, a crucial role is played by certain algebraic moments of the involved kernels, that can be computed by resorting to the their Fourier transform and to the well-known Poisson’s summation formula. By means of the above results we become able to solve the problems of the simultaneous approximation of a function and its derivatives, both from a qualitative and a quantitative point of view, and of the linear prediction by samples from the past.

On Pointwise Approximation Properties of Multivariate Semi-discrete Sampling Type Operators

In this paper multivariate extensions of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally some particular examples are discussed.

A unifying approach for the study of linear sampling type operators in function spaces

AbstractSampling series play a crucial role in Signal and Image Processing. In this note, we illustrate a general method to construct Sampling series and to determine their convergence in Orlicz spaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Rates of approximation for general sampling-type operators in the setting of filter convergence

We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which it is possible to consider several kinds of classical operators, for instance Urysohn integral operators, in particular Mellin-type convolution integrals, and generalized sampling series.We deal with filter convergence, obtaining proper extensions of classical results.

Modular filter convergence theorems for abstract sampling type operators

We study the problem of approximating a real-valued function f by considering sequences of general operators of sampling type, which include both discrete and integral ones. This approach gives a unitary treatment of various kinds of classical operators, such as Urysohn integral operators, in particular convolution integrals, and generalized sampling series.

A unifying approach to convergence of linear sampling type operators in Orlicz spaces

In this paper we give a unified approach to the study of the convergence of a general family of linear sampling type operators which includes several operators very useful in signal reconstruction. We study both the pointwise and uniform convergence and the modular one in the general setting of Orlicz spaces. This creates the possibility of covering several settings such as $L^p$-spaces, the interpolation spaces, the exponential spaces and many others.

Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces

In this paper we introduce a nonlinear version of the Kantorovich sampling type series in a nonuniform setting. By means of the above series we are able to reconstruct signals (functions) which are continuous or uniformly continuous. Moreover, we study the problem of the convergence in the setting of Orlicz spaces: this allows us to treat signals which are not necessarily continuous. Our theory applies to L p -spaces, interpolation spaces, exponential spaces and many others. Several graphical examples are provided.

Approximation properties in abstract modular spaces for a class of general sampling-type operators

In this article we study approximation properties for the class of general integral operators of the form where G is a locally compact Hausdorff topological space, (Hw )w>0 is a net of closed subsets of G with suitable properties and, for every w>0, μ Hw is a regular measure on Hw We give pointwise, uniform and modular convergence theorems in abstract modular spaces and we apply the results to some kind of discrete operators including the sampling-type series.

An Abstract Approach to Sampling-Type Operators inspired by the Work of P.L.Butzer

An Abstract Approach to Sampling-Type Operators inspired by the Work of P.L.Butzer

An Abstract Approach to Sampling-Type Operators inspired by the Work of P.L.Butzer

An Abstract Approach to Sampling-Type Operators inspired by the Work of P.L.Butzer