Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent

Jarosław Kotowicz

Displaying similar documents to “Regularity of the multidimensional scaling functions: estimation of the $L^{p}$ -Sobolev exponent”

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A new technique to estimate the regularity of refinable functions.

Albert Cohen, Ingrid Daubechies (1996)

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We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases. ...

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R. Taberski (1979)

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Connectivity, homotopy degree, and other properties of α-localized wavelets on R.

Gustavo Garrigós (1999)

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In this paper, we study general properties of α-localized wavelets and multiresolution analyses, when 1/2 < α ≤ ∞. Related to the latter, we improve a well-known result of A. Cohen by showing that the correspondence m → φ' = Π m(2 ·), between low-pass filters in H(T) and Fourier transforms of α-localized scaling functions (in H(R)), is actually a homeomorphism of topological spaces. We also show that the space of such filters can be regarded as a connected infinite...

Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

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Ferenc Móricz (1989)

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On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

Displaying similar documents to “Regularity of the multidimensional scaling functions: estimation of the L p -Sobolev exponent”

Displaying similar documents to “Regularity of the multidimensional scaling functions: estimation of the $L^{p}$ -Sobolev exponent”