On a property of continuous solutions of the dilation equation with positive coefficients
On a Theorem of Ingham.
On Discrete and Continous Norms in Paley-Wiener Spaces and Consequences for Exponential Frames.
On Discrete Frames Associated with Semidirect Products.
On extension of Gabor transform to Boehmians
On infinitely smooth almost-wavelets with compact support.
There are known wavelets with exponential decay on infinity [2,3,4] and wavelets with compact support [5]. But these functions have finite smoothness. It is known that there do not exist infinitely differentiable compactly supported wavelets.
On Multiresolution Analysis (MRA) Wavelets in ...
On multiscale denoising of spherical functions: basic theory and numerical aspects.
On Orthogonal Wavelets with the Oversampling Property.
On orthonormal product systems.
On the -problem in Weyl-Heisenberg frames
Let . We investigate the characterization problem which asks for a classification of all the triples such that the Weyl-Heisenberg system is a frame for . It turns out that the answer to the problem is quite complicated, see Gu and Han (2008) and Janssen (2003). Using a dilation technique, one can reduce the problem to the case where and only let and vary. In this paper, we extend the Zak transform technique and use the Fourier analysis technique to study the problem for the case of...
On the adaptive wavelet estimation of a multidimensional regression function under -mixing dependence: Beyond the standard assumptions on the noise
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....
On the computation of scaling coefficients of Daubechies' wavelets
In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
On the decay properties of the Franklin analyzing wavelet
On the discrete wavelet transform of stochastic processes.
On the exact values of coefficients of coiflets
In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients...
On the existence of a compactly supported -solution for two-dimensional two-scale dilation equations
Necessary and sufficient conditions for the existence of compactly supported -solutions for the two-dimensional two-scale dilation equations are given.
On the existence of wavelets for non-expansive dilation matrices.
Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...
On the generalized Morrey spaces.
On the Heisenberg-Pauli-Weyl inequality.