Unconditional biorthogonal wavelet bases in $L^{p}(ℝ^{d})$

• Autorzy: Waldemar Pompe
• Języki publikacji: EN

Abstrakty

EN

We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces $L^{p}(ℝ^{d})$ with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B15: Summability and bases
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 92
• Numer: 1
• Strony: 19-34

Daty

wydano

2002

Twórcy

autor

Waldemar Pompe

• FB Mathematik, AG6, Schloßgartenstr. 7, 64289 Darmstadt, Germany

Identyfikatory

DOI

10.4064/cm92-1-2