Convergence and Summability of Gabor Expansions at the Nyquist Density.
Coorbit space theory for quasi-Banach spaces
We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces , 0 < p,q ≤ ∞.
Corrigendum to 'A Note on Wavelets and S-asymptotics'
Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform
We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary representation...
Daubechies wavelets on intervals with application to BVPs
In this paper, Daubechies wavelets on intervals are investigated. An analytic technique for evaluating various types of integrals containing the scaling functions is proposed; they are compared with classical techniques. Finally, these results are applied to two-point boundary value problems.
Decomposition systems for function spaces
Let be a decomposition system for indexed over D, the set of dyadic cubes in , and a finite set E, and let be the corresponding dual functionals. That is, for every , . We study sufficient conditions on Θ,Θ̃ so that they constitute a decomposition system for Triebel-Lizorkin and Besov spaces. Moreover, these conditions allow us to characterize the membership of a distribution f in these spaces by the size of the coefficients , e ∈ E, I ∈ D. Typical examples of such decomposition systems...
Density estimation with quadratic loss: a confidence intervals method
We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...
Designing Multiresolution Analysis-type Wavelets and Their Fast Algorithms.
Determination of the number of texture segments using wavelets.
Developments from nonharmonic Fourier series.
Dimension functions, scaling sequences, and wavelet sets
The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method provides a completely...
Discrete differential operators in multidimensional Haar wavelet spaces.
Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual.
Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I.
Estimates, Decay Properties, Computation of the Dual Function for Gabor Frames.
Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.
The aim of this paper is the study of the convergence of algorithms involved in the resolution of two scale equations. They are fixed point algorithms, often called cascade algorithms, which are used in the construction of wavelets. We study their speed of convergence in Lebesgue and Besov spaces, and show that the quality of the convergence depends on two independent factors. The first one, as we could foresee, is the regularity of the scaling function which is the solution of the equation. The...
Evidence of intermittency in the local field potentials recorded from patients with Parkinson's disease: a wavelet-based approach.
Exact controllability of shells in minimal time
We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].
Exceptional Sets and Wavelet Packets Orthonormal Bases.
Exponentially decaying wavelets with uncertainty constants uniformly bounded with respect to the smoothness parameter.