Wavelet transforms in generalized Fock spaces.
Wavelet-based quantum field theory.
Wavelets
Wavelets and the complete invariance property
Wavelets as Unconditional Bases in L...(...).
Wavelets for time series analysis - a survey and new results
Wavelets, Generalized White Noise and Fractional Integration: The Synthesis of Fractional Brownian Motion.
Wavelets generated by the Rudin-Shapiro polynomials
In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.
Wavelets obtained by continuous deformations of the Haar wavelet.
One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show...
Wavelets on fractals.
We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [0,1], the Hilbert space is a separable subspace of L2(R, (dx)s) where s = log3(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.
Wavelets on Fractals and Besov Spaces.
Wavelets on general lattices, associated with general expanding maps of .
Wavelets on the integers.
In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2 = TD. We...
Wavelets on the interval and related topics.
Wavelets with composite dilations.
Wavelet-type frames and wavelet-type bases.
Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces
We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class . The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.
When is the last degree solution of a Bézout identity nonnegative on the interval [-1,1]?
We give conditions such that the least degree solution of a Bézout identity is nonnegative on the interval [-1,1].
Why minimax is not that pessimistic
In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...