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Mercerian theorems involving Cesàro and Hölder means of positive order
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Published/Copyright:
September 25, 2009
For a sequence–to–sequence transformation defined by a matrix A denote by μ(A) the set of complex numbers μ such that I − μA is Mercerian, i.e., equivalent to convergence; in particular let Dα = μ(Cα) and Eα = μ(Hα), where Cα and Hα are the Cesàro and Hölder matrices of positive order α, respectively. We prove Dα ⊂ Eα for 0 < α < 1, and Eα ⊂ Dα for α > 1, as has been conjectured by B. Kuttner [3].
Key words and phrases: Mercerian theorems; Cesàro method; Hölder method; spectra of Cesàro and Hölder matrices
Received: 2007-10-14
Published Online: 2009-9-25
Published in Print: 2008-7-1
© Oldenbourg Wissenschaftsverlag
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Keywords for this article
Mercerian theorems;
Cesàro method;
Hölder method;
spectra of Cesàro and Hölder matrices
Articles in the same Issue
- Maximal cluster sets on spaces of holomorphic functions
- On uniqueness of meromorphic functions sharing three sets
- On a differential inequality
- Infinitesimal resistance metrics on Sierpinski gasket type fractals
- Region of variability for concave univalent functions
- Absolutely convergent multiple Fourier series and multiplicative Zygmund classes of functions
- Mercerian theorems involving Cesàro and Hölder means of positive order
- On some high indices theorems III
