Calderón's conditions and wavelets.
The paper presents the proof of the fact that the discrete Calderón condition characterizes the completeness of an orthonormal wavelet basis.
Calderón's reproducing formula for Hankel convolution.
Carleson measures, trees, extrapolation, and T(b) theorems.
The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation...
Characterization of Biothogonal Cosine Wavelets.
Characterization of generators for multiresolution analyses with composite dilations.
Characterization of low pass filters in a multiresolution analysis
We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map A: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ and all (complex) eigenvalues of A have modulus greater than 1. This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which...
Characterization of L...(R...) Using Gabor Frames.
Characterizations of Gabor Systems via the Fourier transform.
We give characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems. The conditions we propose are stated in terms of equations for the Fourier transforms of the Gabor system's generating functions.
Characterizations of tight frame wavelets with special dilation matrices.
Clifford-Hermite Wavelets in Euclidean Space.
Closure of dilates of shift-invariant subspaces
Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a...
Compactly Supported Refinable Distributions in Triebel-Lizorkin Spaces and Besov Spaces.
Comparison of wavelet approximation order in different smoothness spaces.
Comportement asymptotique dans l'algorithme de transformée en ondelettes. Lien avec la régularité de l'ondelette.
We study the asymptotic performance for a Wavelets Transform, in particular as a function of the regularity order of the wavelet.
Compression on the digital unit sphere.
Computation with wavelets in higher dimensions.
Connectivity, homotopy degree, and other properties of α-localized wavelets on R.
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' = Π1∞ m(2−j ·), between low-pass filters in Hα(T) and Fourier transforms of α-localized scaling functions (in Hα(R)), is actually a homeomorphism of topological spaces. We also show that the space of such filters can be regarded as a connected infinite dimensional manifold,...
Construction de bases orthonormées d'ondelettes
Construction of functions with prescribed Hölder and chirp exponents.
We show that the Hölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general, Hölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients; the optimality is the direct consequence...
Construction of non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.
By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.