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Selçuk Journal
of
Applied Mathematics
SPECIAL ISSUE
Summer-Autumn, 2001
Volume 2
Number 2
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2001, Volume 2 - Number 2
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Best approximation and hierarchical bases
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Vladimir L. Vaskevich |
Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
email: vask@math.nsc.ru
Received: October 31, 2001
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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. |
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Key
words
hierarchical bases, reflexive Banach spaces, best approximation,
reproducing mappings, extremal functions of cubature formulas, splines of
affine varieties
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Mathematics Subject Classification (1991): 41A55, 46N05,
65D32
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Article
in PS format (221 kb) |
Article in ZIP
format (80 kb) |
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