Problèmes de pseudo-périodicité
Problems from probability theory
Problems on averages and lacunary maximal functions
We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an regularity result...
Product rule and chain rule estimates for the Hajłasz gradient on doubling metric measure spaces
We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.
Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.
We show that (bi-orthogonal) wavelet bases associated to a dilation matrix which is compatible with integer shifts are generally provided by a multi-resolution analysis. The proof is done by studying the projectors which commute with integer shifts.
Proof of a Conjecture on the Supports of Wigner Distributions.
Proper moving average representations and outer functions in two variables.
Properties of bounded orthonormal spline bases
Properties of certain improper integrals
Properties of extremal sequences for the Bellman function of the dyadic maximal operator
We prove a necessary condition that has every extremal sequence for the Bellman function of the dyadic maximal operator. This implies the weak- uniqueness for such a sequence.
Properties of refinable measures.
We give some new properties of refinable measures and survey results on their asymptotic normality. We also give a survey on the asymptotically optimal time-frequency localisation of refinable measures and associated wavelets.
Pseudo-orthogonal polynomials.
Quadrature formulas based on the scaling function
The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties and . So, in this sense, its choice is optimal. Numerical examples are given.
Quadrature Formulas for Oscillatory Integral Transforms.
Quadrature formulas for rational functions.
Quadrature-free quasi-interpolation on the sphere.
Quantized orthonormal systems: A non-commutative Kwapień theorem
The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is...
Quasi Sure Version of a Theorem of Littlewood.
Quasicrystals and almost periodic functions
We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.
Quasi-definiteness of generalized Uvarov transforms of moment functionals.