1,720,999 research outputs found
Convergence and high order of approximation by Steklov sampling operators
No full textIn this paper we introduce a new class of sampling-type operators, named Steklovsampling operators. The idea is to consider a sampling series based on a kernel functionthat is a discrete approximate identity, and which constitutes a reconstruction processof a given signalf, based on a family of sample values which are Steklov integrals oforderrevaluated at the nodesk/w,k is an element of Z,w>0. The convergence properties of theintroduced sampling operators in continuous functions spaces and in theL(p)-settinghave been studied. Moreover, the main properties of the Steklov-type functions havebeen exploited in order to establish results concerning the high order of approximation.Such results have been obtained in a quantitative version thanks to the use of thewell-known modulus of smoothness of the approximated functions, and assumingsuitable Strang-Fix type conditions, which are very typical assumptions in applicationsinvolving Fourier and Harmonic analysis. Concerning the quantitative estimates, weproposed two different approaches; the first one holds in the case of Steklov samplingoperators defined with kernels with compact support, its proof is substantially basedon the application of the generalized Minkowski inequality, and it is valid with respectto thep-norm, with 1 <= p <=+infinity. In the second case, the restriction on the supportof the kernel is removed and the corresponding estimates are valid only for 1<=+infinity. Here, the key point of the proof is the application of the well-known Hardy-Littlewood maximal inequality. Finally, a deep comparison between the proposedSteklov sampling series and the already existing sampling-type operators has beengiven, in order to show the effectiveness of the proposed constructive method ofapproximation. Examples of kernel functions satisfying the required assumptions havebeen provided
An efficient asymptotic-numerical method to solve nonlinear systems of one-dimensional balance laws
No full textApproximation by Max-Product Neural Network Operators of Kantorovich Type
No full textIn the present paper, we develop the theory of max-product neural network operators in a Kantorovich-type version, which is suitable in order to study the case of Lp-approximation for not necessarily continuous data. Moreover, also the case of the pointwise and uniform approximation of continuous functions is considered. Finally, several examples of sigmoidal functions for which the above theory can be applied are presented
Pointwise and uniform approximation by multivariate neural network operators of the max-product type
No full textn this article, the theory of multivariate max-product neural network (NN) and quasi-interpolation operators has been introduced. Pointwise and uniform approximation results have been proved, together with estimates concerning the rate of convergence. At the end, several examples of sigmoidal activation functions have been provided
Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing
No full textIn this paper we study a nonlinear version of the Sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces \Lphi that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in -spaces, -spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included
Approximation by Multivariate Generalized Sampling Kantorovich Operator in the Setting of Orlicz Spaces
No full textIn this paper we study a linear version of the Sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). We alos study the modular convergence of these operators in the setting of Orlicz spaces \Lphi that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in -spaces, -spaces and exponential spaces follow as particular cases. Several graphical representations are included
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