Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability

Werner Balser; Andreas Beck

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1349-1357
  • ISSN: 0373-0956

Abstract

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For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above

How to cite

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Balser, Werner, and Beck, Andreas. "Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability." Annales de l'institut Fourier 46.5 (1996): 1349-1357. <http://eudml.org/doc/75216>.

@article{Balser1996,
abstract = {For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above},
author = {Balser, Werner, Beck, Andreas},
journal = {Annales de l'institut Fourier},
keywords = {general matrix summability methods; multisummability; power series; matrix methods},
language = {eng},
number = {5},
pages = {1349-1357},
publisher = {Association des Annales de l'Institut Fourier},
title = {Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability},
url = {http://eudml.org/doc/75216},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Balser, Werner
AU - Beck, Andreas
TI - Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1349
EP - 1357
AB - For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above
LA - eng
KW - general matrix summability methods; multisummability; power series; matrix methods
UR - http://eudml.org/doc/75216
ER -

References

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  1. [1] W. BALSER, From Divergent Power Series to Analytic Functions, Lecture Notes in Mathematics 1582, Springer-Verlag, 1994. Zbl0810.34046MR96d:34071
  2. [2] A. BECK, Matrix-Summationsverfahren und Multisummierbarkeit, Dissertation, Ulm, 1995. Zbl0848.40004
  3. [3] G.H. HARDY, Note on a divergent series, Proc. Cambridge Phil. Soc., (1941), 1-8. Zbl0027.10101MR2,278aJFM67.0200.02
  4. [4] G.H. HARDY, Divergent Series, Oxford, 1956. 
  5. [5] W.B. JURKAT, Summability of asymptotic power series, Asympt. Anal., 7 (1993), 239-250. Zbl0802.30002MR95d:40016
  6. [6] B. MALGRANGE, Sommation des séries divergentes, Expo. Math., 13 (1995), 163-222. Zbl0836.40004MR96i:34125

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