On the "Collective Hausdorff Method"

1950 ◽  
Vol 1 (1) ◽  
pp. 66
Author(s):  
W. H. J. Fuchs
Keyword(s):  
Hausdorff Method

A Best Possible Tauberian Theorem for the Collective Continuous Hausdorff Summability Method

1971 ◽  
Vol 23 (3) ◽  
pp. 544-549
Author(s):  
G. E. Peterson
Keyword(s):  
Hausdorff Spaces ◽  
Locally Compact ◽  
Compact Spaces ◽  
Bounded Complex ◽  
Hausdorff Method ◽  
Borel Functions ◽  
Bounded Functions ◽  
Abelian Theorem ◽  
Complex Valued ◽  
Locally Compact Spaces

The purpose of this paper is to prove that o(l/x) is the best possible Tauberian condition for the collective continuous Hausdorff method of summation. The analogue of this result for the collective (discrete) Hausdorff method is known [1, pp. 229, ff.; 7, p. 318; 8, p. 254]. Our method involves generalizing a well-known Abelian theorem of Agnew [2] to locally compact spaces and then applying the analogue for integrals of a result Lorentz obtained for series [6, Theorem 1].Let T and X denote locally compact, non compact, σ-compact Hausdorff spaces. Let T′ = T ∪ (∞) and X′ = X ∪ (∞) denote the onepoint compactifications of T and X, respectively. Let B(T) denote the set of locally bounded, complex valued Borel functions on T and let B∞(T) denote the bounded functions in B(T).

Absolute summability functions for Hausdorff methods

1982 ◽  
Vol 91 (1) ◽  
pp. 51-56
Author(s):  
B. Kuttner
Keyword(s):  
Absolute Summability ◽  
Bounded Sequence ◽  
Summability Method ◽  
Negative Integer ◽  
Hausdorff Method ◽  
The Matrix ◽  
Sequence Transformation ◽  
Image Position

1. Following Lorentz, we suppose throughout that Ω(n) is a non-negati ve non-decreasing function of the non-negative integer n such that Ω(n)→ ∞ as n → ∞. Consider the summability method given by the sequence-to-sequence transformation corresponding to the matrix A = (ank). We say that Ω(n) is a summability function for A (or absolute summability function for A) if the following holds: Any bounded sequence {sn} such that the number of values of ν with ν ≤ n, sν ≠ 0 does not exceed Ω(n) is summable A (or is absolutely summable A, respectively). These definitions are due to Lorentz (4), (6). We shall be concerned with the case in which A is a regular Hausdorff method, say A = H = (H, μn). Then H is given by the matrix (hnk) withwithX(0) = X(0 + ) = 0, X(1) = 1;(see e.g.(1), chapter XI). We shall suppose throughout that these conditions are satisfied. It is known that H is then necessarily also absolutely regular.

scholarly journals Innovation and Personality: A Study of Attitude to Innovation among Krasnoyarsk Students and Business Experts using the Basadur-Hausdorff Method

2015 ◽  
Author(s):  
Maria I. Ilbeykina ◽  
Maria A. Kolesnik ◽  
Natalia M. Libakova ◽  
Ekaterina A. Sertakova ◽  
Alexandra A. Sitnikova
Keyword(s):  
Hausdorff Method

On ‘translated quasi-Cesàro’ summability

1966 ◽  
Vol 62 (4) ◽  
pp. 705-712 ◽  
Author(s):  
B. Kuttner
Keyword(s):  
Cesàro Summability ◽  
Fixed Sequence ◽  
Cesaro Summability ◽  
Hausdorff Method ◽  
The Matrix ◽  
Sequence Transformation ◽  
Image Position

Corresponding to a fixed sequence {μn}, the Hausdorff method of summability (H, μn) is defined by the sequence-to-sequence transformation†where we writeThe quasi-Hausdorff method (H*, μn) is defined by the transformationthus the matrix of the (H*, μn) transformation is the transpose of that of the (H*, μn) transformation. A method introduced by Ramanujan (9), which we will call‡ (S,μn) is given by the transformationThus the elements of row n of the matrix of the (S, μn) transformation are those of the corresponding row of the (H*, μn) transformation moved n places to the left.

scholarly journals On the degree of approximation of functions belonging to the weighted $ (L^p, \xi (t)) $ class by Hausdorff means

2001 ◽  
Vol 32 (4) ◽  
pp. 305-314
Author(s):  
B. E. Rhoades
Keyword(s):  
Mass Function ◽  
Degree Of Approximation ◽  
Approximation Of Functions ◽  
Hausdorff Method ◽  
Hausdorff Means

In this paper we obtain a theorem on the degree of approximation of functions belonging to a certain weighted class, using any Hausdorff method with mass function possessing a derivative. This result is a substantial generalization of the theorem of Lal [2].

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