Related papers: Multivariate semi-discrete sampling type operators…
In this paper, we obtained some global approximation results for general Gamma type operators.
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is…
In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally,…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
In this paper, we extend the r-Dowling polynomials to their bivariate forms. Several properties that generalize those of the bivariate Bell and r-Bell polynomials are established. Finally, we obtain two forms of generalized Spivey's…
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…
The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent…
We derive a Dickman approximation for the small jumps of a large class of multivariate L\'evy processes. We then apply this approximation to develop a simulation method for the class of general multivariate gamma distributions (GMGD). A…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling…
In this paper, we establish new inequalities of Ostrowski type for functions whose derivatives in absolute value are m-convex. We also give some applications to special means of positive real numbers. Finally, we obtain some error estimates…
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order…