Boundedness of the wavelet transform in certain function spaces.
Boundness of Cesàro means operators.
Bounds for Vandermonde type determinants of orthogonal polynomials.
Brushlet characterization of the Hardy space H1(R) and the space BMO.
A typical wavelet system constitutes an unconditional basis for various function spaces -Lebesgue, Besov, Triebel-Lizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelet-type system, called a brushlet system. In [3] it was noticed that brushlets constitute unconditional bases for classical function spaces such as the Triebel-Lizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the...
Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin.
Calderón's conditions and wavelets.
The paper presents the proof of the fact that the discrete Calderón condition characterizes the completeness of an orthonormal wavelet basis.
Calderón's Formula Associated with a Differential Operator on (0, ...) and Inversion of the Generalized Abel Transform.
Calderón's reproducing formula for Hankel convolution.
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.
Carleson measures, trees, extrapolation, and T(b) theorems.
The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation...
Chain sequences and compact perturbations of orthogonal polynomials.
Characteristic functions and -orthogonality properties of Chebyshev polynomials of third and fourth kind.
Characterization of Bessel sequences.
Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.
Characterization of Biothogonal Cosine Wavelets.
Characterization of Fourier Transforms of Vector Valued Functions and Measures
Characterization of generators for multiresolution analyses with composite dilations.
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 Gabor Systems via the Fourier transform.
We give characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems. The conditions we propose are stated in terms of equations for the Fourier transforms of the Gabor system's generating functions.
Characterizations of tight frame wavelets with special dilation matrices.