Calderón's Formula Associated with a Differential Operator on (0, ...) and Inversion of the Generalized Abel Transform.
Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces
We study sufficient conditions on the weight w, in terms of membership in the classes, for the spline wavelet systems to be unconditional bases of the weighted space . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.
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 tight frame wavelets with special dilation matrices.
Chirps -dimensionnels et analyse -microlocale
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...
Commutators based on the Calderón reproducing formula
We prove the Schatten-Lorentz ideal criteria for commutators of multiplications and projections based on the Calderón reproducing formula and the decomposition theorem for the space of symbols corresponding to commutators in the Schatten ideal.
Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators
A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...
Compression of satellite data.
In this paper, we present the simple and double compression algorithms with an error control for compressing satellite data corresponding to several revolutions. The compressions are performed by means of approximations in the norm L∞ by finite series of Chebyshev polynomials, with their known properties of fast evaluation, uniform distribution of the error, and validity over large intervals of time. By using the error control here introduced, the number of terms of the series is given automatically...
Continuity of Calderón-Zygmund operators on the space BMO.
Continuous -frame in Hilbert -modules.
Control norms for large control times
Control Norms for Large Control Times
A control system of the second order in time with control is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as while the –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.
Convergence of Series of Translations.
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 the paper "Pointwise convergence for expansions in surface harmonics of arbitrary dimension".