ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Factorable matrices and their associated Riesz matrices; pp. 379–386

Full article in PDF format | doi: 10.3176/proc.2014.4.03

Author
Maria Zeltser

Abstract

A factorable matrix is a natural generalization of a Riesz matrix. When considering the properties of factorable matrices, many authors have used methods similar to the methods for Riesz matrices. So, a property having a long proof for Riesz matrices generated a long proof for a factorable matrix. In this paper for any factorable matrix we introduced its associated Riesz matrix. With its help many properties of a factorable matrix can be easily and briefly deduced from the corresponding properties of the associated Riesz matrix.


References

  1. Aasma, A. Factorable matrix transforms of summability domains of Cesàro matrices. Int. J. Contemp. Math. Sci., 2011, 6, 2201–2206.

  2. Bennett, G., Boos, J., and Leiger, T. Sequences of 0’s and 1’s. Studia Math., 2002, 149, 75–99.
http://dx.doi.org/10.4064/sm149-1-5

  3. Boos, J. Classical and Modern Methods in Summability. Oxford University Press, New York, Oxford, 2000.

  4. Boos, J. and Leiger, T. On some ‘duality’ of the Nikodym property and the Hahn property. J. Math. Anal. Appl., 2008, 341, 235–246.
http://dx.doi.org/10.1016/j.jmaa.2007.10.023

  5. Boos, J. and Zeltser, M. Sequences of 0’s and 1’s. Classes of concrete ‘big’ Hahn spaces. Z. Anal. Anwendungen, 2003, 22, 819–842.
http://dx.doi.org/10.4171/ZAA/1175

  6. Hardy, G. H. Divergent Series. Clarendon Press, Oxford, 1949.

  7. Hutnjak, S. On Potency of Factorable Matrices. MSc~thesis, Tallinn University, 2013 (in Estonian).

  8. Kuttner, B. and Parameswaran, M. R. Potent conservative summability methods. Bull. London Math. Soc., 1994, 26, 297–302.
http://dx.doi.org/10.1112/blms/26.3.297

  9. Rhoades, B. E. An extension of two results of Hardy. Sarajevo J. Math., 2013, 9, 95–100.
http://dx.doi.org/10.5644/SJM.09.1.08

10. Rhoades, B. E. and Sen, P. Lower bounds for some factorable matrices. Int. J. Math. Math. Sci., 2006, Art. ID 76135, 1–13.

11. Zeltser, M. Bounded domains of generalized Riesz methods with the Hahn property. J. Funct. Space. Appl., 2013, Art. ID 908682, 1–8.


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