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Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

100%

Behera B.

Colloquium Mathematicum

2014

tom 136

nr 2

149-168

We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for $L^{p}(K)$, 1 < p < ∞. We also prove that this system, normalized in $L^{p}(K)$, is a democratic basis of $L^{p}(K)$. This also proves that the Haar system is a greedy basis of $L^{p}(K)$ for 1 < p < ∞.

Non-MSF Wavelets for the Hardy Space H²(ℝ)

100%

Behera B.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 2

169-178

All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Colloquium Mathematicum

2 Behera B.

1 2014

1 2004

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Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

Non-MSF Wavelets for the Hardy Space H²(ℝ)