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

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

We show that in $L_1(\R)$ 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.

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2008-03, Vol.144 (2), p.499-510
Hauptverfasser: GOGYAN, SMBAT, WOJTASZCZYK, P.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
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Zusammenfassung:We show that in $L_1(\R)$ 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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004107000886