Selšuk Journal of Applied Mathematics

www.selcuk.edu.tr




 Selšuk Journal of
  Applied Mathematics

SPECIAL ISSUE

 
Summer-Autumn, 2001
  Volume  2
  Number 2

 
Research Center of 
  Applied Mathematics


 SJAM Summer-Autumn 2001, Volume 2 - Number 2

Best approximation and hierarchical bases

Vladimir L. Vaskevich
Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
email: vask@math.nsc.ru

Received: October 31, 2001
 

Summary
In the present paper we extend the definition of a hierarchical basis to the case of Banach spaces with higher smoothness order elements. Hierarchical bases are similar to the well-known Faber-Schauder system. We prove that there exists a hierarchical basis of the Banach space under consideration. We study the interplay between hierarchical bases and solutions to specific problems of best approximation. The construction of some hierarchical basis is finally described.

 

Key words
hierarchical bases, reflexive Banach spaces, best approximation, reproducing mappings, extremal functions of cubature formulas, splines of affine varieties
 

Mathematics Subject Classification (1991): 41A55, 46N05, 65D32
 
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