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Given and a sequence of Dirichlet polynomials estimates for the coefficientsa n? are proved if {tn} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for theA-transforms of the geometric sequence; moreover a Jentzsch type theorem for {tn(z)} is derived.

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In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.

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Abstract  

The aim of this paper is to give weighted function spaces in which the sequence of Cesàro means of the Jacobi-Fourier series are uniformly convergent. Error estimate for the approximation will also be considered.

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Abstract  

The concepts of subsequence and rearrangement of double sequence are used to present multidimensional analogues of the following core questions. If x is a bounded real sequence and A is a matrix summability method, under what conditions does there exist y, a subsequence (rearrangement) of x such that each number t in the core of x is a limit point of Ay?

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Authors: B. Della Vecchia, G. Mastroianni, L. Szili and P. Vértesi

Abstract

This paper generalizes some results of L. B. Golinskii [4] on the asymptotic behaviour of reflection coefficients associated with generalized Jacobi weight functions.

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Abstract  

We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for exponential weights, where the weights are not necessarily symmetric.

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Abstract  

The weighted averages of a sequence (c k), c k ∈ ℂ, with respect to the weights (p k), p k ≥ 0, with {fx135-1} are defined by {fx135-2} while the weighted average of a measurable function f: ℝ+ → ℂ with respect to the weight function p(t) ≥ 0 with {fx135-3}. Under mild assumptions on the weights, we give necessary and sufficient conditions under which the finite limit σ nL as n → ∞ or σ(t) → L as t → ∞ exists, respectively. These characterizations may find applications in probability theory.

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Abstract  

As pointed out in [4] the paper [2], authored by G. Bennett, J. Boos and T. Leiger, contains a nontrivial gap in the argumentation of the proof of Theorem 5.2 which is one of main results of that paper and has been applied three times. Till now neither the gap is closed nor a counterexample has been stated. That is why the authors have examined in [4] the situation around the ‘gap’ aiming to a better understanding for the gap. The aim of this paper is to prove the mentioned applications of the theorem in doubt by using gliding hump arguments (quite similar to the classical proofs of the Theorems of Schur and Hahn in the first case (cf. [3]) and a very technical and artful construction, being of independent mathematical interest, in the second case).

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