Asyptotic Behaviour of Multiperiodic Functions G(x) = ... g (x/2...).
Banach algebras of pseudodifferential operators and their almost diagonalization
We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we associate a symbol class . Then every operator with a symbol in is almost diagonal with respect to special wave packets (coherent states or Gabor frames), and the rate of almost diagonalization is described precisely by the underlying convolution algebra...
Bases d'ondelettes sur les courbes corde-arc, noyau de Cauchy et spaces de Hardy associés.
Se construyen dos bases incondicionales de L2(R) adaptadas al estudio de la integral de Cauchy sobre una curva cuerda-arco, y se extiende la construcción a L2(Rd). Esto permite obtener una prueba simple del "Teorema T(b)" de G. David, J.L. Journé u S. Semmes. Se define un espacio de Hardy ponderado Hb1(Rd) caracterizado por las bases anteriores. Finalmente se aplican estos métodos al estudio del potencial de doble capa sobre una superficie lipschitziana.
Bases orthonormées de paquets d'ondelettes.
BCR algorithm and the T(b) Theorem.
Besov characteristic of a distribution.
Beurling-Landau-Type Theorems for Non-Uniform Sampling in Shift Invariant Spline Spaces.
BIlinear Operators with Non-Smooth Symbol, I.
Biorthogonal multiresolution analyses and decompositions of Sobolev spaces.
Biorthogonal Wavelets in H...(...).
Biorthogonal wavelets, MRA's and shift-invariant spaces
We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity D entirely in terms of the dimension function. This improves the previous characterization in [8] removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in [17].
Boundedness of the wavelet transform in certain function spaces.
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...
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 reproducing formula for Hankel convolution.
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...
Characterization of Biothogonal Cosine Wavelets.
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.