A note of dilations inLp

Subdivision schemes inLp spaces

Subdivision schemes play an important role in computer graphics and wavelet analysis. In this paper we are mainly concerned with convergence of subdivision schemes in Lp spaces (1 ≤ p ≤ ∞). We characterize the Lp-convergence of a subdivision scheme in terms of the p-norm joint spectral radius of two matrices associated with the corresponding mask. We also discuss various properties of the limit...

InlP, a New Virulence Factor with Strong Placental Tropism.

Intrauterine infection is a major detriment for maternal-child health and occurs despite local mechanisms that protect the maternal-fetal interface from a wide variety of pathogens. The bacterial pathogen Listeria monocytogenes causes spontaneous abortion, stillbirth, and preterm labor in humans and serves as a model for placental pathogenesis. Given the unique immunological environment of the ...

Paschke Dilations

Wavelets with Composite Dilations

A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L2(Rn) under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets A and B. Typically, the members of B are shear matrices (all eigenvalues are one) while the members of A are matrices expanding or contracting on a proper subspace of Rn...

Orthonormal Dilations of Parseval Wavelets

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...