Über das Lokalisierungsprinzip bei mehrdimensionalen Shannonschen und konjugierten Shannonschen Abtastreihen
Unconditional biorthogonal wavelet bases in
We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces 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.
Unique Reconstruction of Band-limited Signals by a Mallat-Zhong Wavelet Transform Algorithm.
Vanishing moments for scaling vectors.
Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)
We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates.
Wandering Sets for a Class of Borel Isomorphisms of ...0,1).
Wavelet Analysis and Covariance Structure of some Classes of Non-Stationary Processes.
Wavelet analysis of the multivariate fractional brownian motion
The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behaviour of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral...
Wavelet analysis on a Boehmian space.
Wavelet approximation methods for pseudodifferential equations: I. Stability and convergence.
Wavelet based numerical homogenization.
Wavelet bases in
It is shown that an orthonormal wavelet basis for associated with a multiresolution is an unconditional basis for , 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.
Wavelet Basis Packets and Wavelet Frame Packets.
Wavelet constructions in non-linear dynamics.
Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the original...
Wavelet frames for distributions; local and pointwise regularity
This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.
Wavelet Frames on Lipschitz Curves and Applications.
Wavelet packets on locally compact abelian groups.
Wavelet Sets in ...
Wavelet techniques for pointwise regularity
Let be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with , and denoted by . We show how properties of are transferred into properties of . Applications are given in multifractal analysis.