In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and external force. Based on Schauder’s fixed point theorem, we establish sufficient conditions for existence uniqueness of global Banach spaces. Moreover, polynomial decay estimate is given. Furthermore, approximate controllability obtained by const...

Microlocal defect measures for Cauchy data of Dirichlet, resp. Neumann, eigenfunctions an ellipse $E$ are determined. We prove that, any invariant curve the billiard map on boundary phase space $B^\* E$ ellipse, there exists a sequence whose concentrates curve. use this result to give new proof that ellipses infinitesimally spectrally rigid among $C^\\infty$ domains with symmetries ellipse.

Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is given for each rule. In addition, two theorems, containing sufficient conditions for the convergence of the sequence of quadrature rules to the integ...

Let (x n) be a bounded sequence in a Banach space X. Rosenthal's l 1-theorem states that there is essentially only one exceptional situation where it is not possible to extract a subsequence which is a weak Cauchy sequence: This happpens if (x n) is the sequence of unit vectors in l 1. The aim of these lectures is twofold: On the one hand results from the last few years centering around this th...

The existence of solutions of the inhomogeneous Cauchy-Riemann equations as a powerful tool in the study of analytic functions of several complex variables is well demonstrated in t h e monograph [22] of L. H6rmander. The main objective of this expository paper is to show how this technique can be used tO Unify and simplify the study of interpolation problems for entire functions of one complex...

Conditions on 7c and / are given for the pointwise and uniform convergence to the Cauchy principal value integral rmm _1<A<1, j-i x~x of a sequence of integrals of piecewise linear approximations to f(x) or g\(x) = (f(x) — f(X))/(x — A). The important special case, k(x) = (1 a;)a(l + x)13, is considered in detail.

Analogous to Ershov’s hierarchy for ∆2-subsets of natural numbers we discuss the similar hierarchy for recursively approximable real numbers. Namely, we define the k-computability for natural number k and f -computability for function f . We will show that these notions are not equivalent for different representations of real numbers based on Cauchy sequence, Dedekind cut and binary expansion.

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...