Non-MSF wavelets for the Hardy space H^2(R)

• Autorzy: Behera B.
• Języki publikacji: EN

Abstrakty

EN

All wavelets constructed so far for the Hardy space H^2(R) are MSF wavelets. We construct a family of H^2-wavelets which are not MSF. An equivalence relation on H^2-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H^2-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Słowa kluczowe

EN

wavelet; MSF wavelet; wavelet set; H^2-wavelet; H^2-MSF wavelet; H^2-wavelet set

PL

falka; zbiór falkowy; H^2-falka; H^2-zbiór falkowy

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 169--178
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Behera B.

Bibliografia

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• [2] P. Auscher, Solution of two problems on wavelets, ibid. 5 (1995), 181-236.
• [3] B. Behera, Band-limited wavelets and wavelet packets, PhD thesis, Indian Institute of Technology, Kanpur, 2001.
• [4] B. Behera and S. Madan, Wavelet subspaces invariant under groups of translation operators, Proc. Indian Acad. Sci. Math. Sci. 113 (2003), 171-178.
• [5] Y.-H. Ha, H. Kang, J. Lee and J. Seo, Unimodular wavelets for L2 and the Hardy space H2, Michigan Math. J. 41 (1994), 345-361.
• [6] E. Hernández and G. L. Weiss, A First Course on Wavelets, CRC Press, Boca Raton, 1996.
• [7] G. Majchrowska, Some new examples of wavelets in the Hardy space H2(R), Bull. Polish Acad. Sci. Math. 49 (2001), 141-149.
• [8] S. Schaffer and E. Weber, Wavelets with the translation invariance property of order n, preprint, 2001.
• [9] E. Weber, On the translation invariance of wavelet subspaces, J. Fourier Anal. Appl. 6 (2000), 551-558.