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.
Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets
Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].
Constructions de bases orthonormées d'ondelettes.
Constructive function theory and spline systems
Continous Wavelet Transforms with Applications to Analyzing Functions on Spheres.
Continuity of Calderón-Zygmund operators on the space BMO.
Continuous dependence of solutions for ill-posed evolution problems.
Continuous -frame in Hilbert -modules.
Continuous rearrangements of the Haar system in for 0 < p < ∞
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
Continuous symmetrized Sobolev inner products of order . II.
Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.
In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
Contributions to local and microlocal analysis, an overwiew
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 and Summability of Gabor Expansions at the Nyquist Density.
Convergence in norm of the Fejér means on with respect to Walsh-Kaczmarz system.
Convergence of Cesàro means of functions with respect to unbounded Vilenkin systems.
Convergence of Fourier series with respect to multiplicative systems and the -fluctuation continuity modulus.