Chirps -dimensionnels et analyse -microlocale
Ciesielski and Franklin systems
A short survey of results on classical Franklin system, Ciesielski systems and general Franklin systems is given. The principal role of the investigations of Z. Ciesielski in the development of these three topics is presented. Recent results on general Franklin systems are discussed in more detail. Some open problems are posed.
Classical 2-orthogonal polynomials and differential equations.
Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials
In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.
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...
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.
Compact Jacobi matrices : from Stieltjes to Krein and
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...
Compactly Supported Refinable Distributions in Triebel-Lizorkin Spaces and Besov Spaces.
Comparison of wavelet approximation order in different smoothness spaces.
Completeness in L1(R) of discrete translates.
We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.
Complex and distributional weights for sieved ultraspherical polynomials.
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 and restoration of square integrable functions.
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...
Compression on the digital unit sphere.
Computation with wavelets in higher dimensions.
Computer graphics and a new Gibbs phenomenon for Fourier-Bessel series.
Concepts of generalized bounded variation and the theory of Fourier series.