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International Journal of Mathematics and Mathematical Sciences
Volume 2013, Article ID 748645, 11 pages
Research Article

Admissible Differential Bases in Banach Spaces

Yaroslavl State University, Sovetskaya Street 14, Yaroslavl 150000, Russia

Received 27 February 2013; Accepted 2 July 2013

Academic Editor: Marco Squassina

Copyright © 2013 Evgenii I. Berezhnoj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present work, a new method for constructing differential bases is presented. The bases constructed by this method allow us to distinguish symmetric spaces with different behaviour of fundamental functions at zero, as in the case of Hayes and Stokolos, and even allow us to distinguish Lorentz and Marzinkiewicz spaces or Lebesgue and Marzinkiewicz spaces whose fundamental functions are the same.