Related papers: A generalization of the exponential sampling serie…
In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We analyse the approximation properties of the bivariate generalization of the family of Kantorovich type exponential sampling series. We derive the point-wise and Voronovskaya type theorem for these sampling type series. Using the modulus…
Here we provide a unifying treatment of the convergence of a general form of sampling type operators, given by the so-called Durrmeyer sampling type series. In particular we provide a pointwise and uniform convergence theorem on…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed…
In this paper, we introduce Mellin-Steklov exponential samplingoperators of order $r,r\in\mathbb{N}$, by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded…
Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function in BT can be approximated by an element in a…
This article discusses the convergence properties of the Max Product and Max Min variants of Durrmeyer type exponential sampling series. We first establish pointwise and uniform convergence of both operators in the space of log uniformly…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…