Abstract In this note, we spotlight a generalization of Weierstrass integral operators introduced by Eugeniusz Wachnicki. The construction involves modified Bessel functions. are correlated with diffusion equation. Our main result consists in obtaining the asymptotic expansion derivatives any order Wachnicki’s operators. All coefficients explicitly calculated, and distinct expressions provided ...

Let C be a non-degenerate planar curve. We show that the curve is of Khintchine-type for convergence in the case of simultaneous approximation in R 2 with two independent approximation functions; that is if a certain sum converges then the set of all points (x, y) on the curve which satisfy simultaneously the inequalities qx < ψ1(q) and qy < ψ2(q) infinitely often has induced measure 0. This co...

For an undirected edge-weighted graph $G$ and a set $R$ of pairs vertices called terminals, multicut is edges such that removing these from disconnects each pair in $R$. We provide algorithm computing $(1+\varepsilon)$-approximation the minimum time $(g+t)^{(O(g+t)^3)}\cdot(1/\varepsilon)^{O(g+t)} \cdot n \log n$, where $g$ genus $t$ number terminals. This tight several aspects, as problem both...

A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they...