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On weak non-equivalence of wavelet–like systems in L1†

Published online by Cambridge University Press:  01 March 2008

SMBAT GOGYAN  and
P. WOJTASZCZYK
SMBAT GOGYAN
Affiliation:
Institut of Mathematics, Armenian National Academy of Sciences, Marshal Baghramian ave. 24b, 375019 Yerevan, Armenia. e-mail: smbatino@freenet.am
P. WOJTASZCZYK
Affiliation:
Institut of Applied Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland. e-mail: wojtaszczyk@mimuw.edu.pl
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Abstract

We show that in the Haar wavelet basis is not equivalent to any permutation with any signs of the Strω wavelet basis. We also construct a Haar-type system in L1[0,1] which is not equivalent to any subsequence with signs of the classical Haar basis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 499 - 510
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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