Abstract
We show that there exit E-J generalized Hausdorff matrices and unbounded sequences such that each matrix has convergence domain .
Highlights
The convergence domain of an infinite matrix A ank n, k 0, 1, . . . will be denoted byA and is defined by A : {x {xn} | An x ∈ c}, where c denotes the space of convergence sequences, An x : k ankxk
In 1967, Rhoades 9 showed that the convergence domain of every known prime Hausdorff matrix is of the form c ⊕ x for a particular unbounded sequence x
The main result of this paper is to show that there exist E-J generalized Hausdorff matrices Hμα whose moment sequences are μnα n n
Summary
The convergence domain of an infinite matrix A ank n, k 0, 1, . . . will be denoted byA and is defined by A : {x {xn} | An x ∈ c}, where c denotes the space of convergence sequences, An x : k ankxk. From 1 or 3 a E-J generalized Hausdorff matrix for α > 0 is regular if and only if there exists a function χ ∈ BV 0, 1 with χ 1 − χ 0 1 such that μnα tn αdχ t , 1.2 in which case χ is called the moment generating function, or mass function, for Hμα and μnα is called moment sequence. In 1967, Rhoades 9 showed that the convergence domain of every known prime Hausdorff matrix is of the form c ⊕ x for a particular unbounded sequence x.
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