Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$

• Autorzy: Paweł Bechler
• Języki publikacji: EN

Abstrakty

EN

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces $L₁(ℝ^d)$ and $BV(ℝ^d)$ are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in $L₁(ℝ^d)$ is also shown.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 26A45: Functions of bounded variation, generalizations
• 26B30: Absolutely continuous functions, functions of bounded variation
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 1
• Strony: 25-37

Daty

wydano

2005

Twórcy

autor

Paweł Bechler

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba53-1-4