Power-series and Hausdorff matrices

Hausdorff Moments, Hardy Spaces and Power Series

In this paper we consider power and trigonometric series whose coefficients are supposed to satisfy the Hausdorff conditions, which play a relevant role in the moment problem theory. We prove that these series converge to functions analytic in cut domains. We are then able to reconstruct the jump functions across the cuts from the coefficients of the series expansions by the use of the Pollacze...

Watson Resummation of a Class of Hausdorff–transformed Power Series

In this paper we study a class of Hausdorff–transformed power series whose convergence is extremely slow for large values of the argument. We perform a Watson–type resummation of these expansions, and obtain, by the use of the Pollaczek polynomials, a new representation whose convergence is much faster. We can thus propose a new algorithm for the numerical evaluation of these expansions, which ...

Constructing Rotation Matrices using Power Series

Concerning Hausdorff Matrices and Absolutely Convergent Sequences1

for£}=0, 1,2,.... This paper is concerned with the determination of those generalized Hausdorff matrices which sum all absolutely convergent sequences. Theorem 2 gives a sufficiency condition stated in terms of the behavior of the points of continuity of the graph of g and Theorems 3 and 4 provide examples which serve to further describe functions which generate such matrices. Theorem 5 gives a...

Hausdorff Matrices as Bounded Operators over /

A necessary and sufficient condition is obtained for an arbitrary Hausdorff matrix to belong to B(l). It is then shown that every conservative quasi-Hausdorff matrix is of type M. Let (H, u) denote the Hausdorff method with generating sequence ¡x = {/L,}, / = {{xn} \2„\xn\ < oo}, B(l) the algebra of bounded linear operators on /. A necessary and sufficient condition is obtained for an arbitrary...