General Haar systems and greedy approximation

• Autorzy: Anna Kamont
• Języki publikacji: EN

Abstrakty

EN

We show that each general Haar system is permutatively equivalent in $L^{p}([0,1])$, 1 < p < ∞, to a subsequence of the classical (i.e. dyadic) Haar system. As a consequence, each general Haar system is a greedy basis in $L^{p}([0,1])$, 1 < p < ∞. In addition, we give an example of a general Haar system whose tensor products are greedy bases in each $L^{p}([0,1]^{d})$, 1 < p < ∞, d ∈ ℕ. This is in contrast to [11], where it has been shown that the tensor products of the dyadic Haar system are not greedy bases in $L^{p}([0,1]^{d})$ for 1 < p < ∞, p ≠ 2 and d ≥ 2. We also note that the above-mentioned general Haar system is not permutatively equivalent to the whole dyadic Haar system in any $L^{p}([0,1])$, 1 < p < ∞, p ≠ 2.

Kategorie tematyczne

• 41A30: Approximation by other special function classes
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A46: Approximation by arbitrary nonlinear expressions; widths and entropy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 145
• Numer: 2
• Strony: 165-184

Daty

wydano

2001

Twórcy

autor

Anna Kamont

• Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland

Identyfikatory

DOI

10.4064/sm145-2-5