Laurent polynomial perturbations of linear functionals. An inverse problem.
Le traitement du signal et l'analyse mathématique
Nous étudons sur des exemples significatifs l’intersection entre le traitement du signal et l’analyse fonctionnelle.
Learning to swim in a sea of wavelets.
L'espace usuel C ne possede aucun R.U.C-systeme orthonorme.
Limit points of eigenvalues of truncated unbounded tridiagonal operators
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
Linear combinations of generators in multiplicatively invariant spaces
Multiplicatively invariant (MI) spaces are closed subspaces of L²(Ω, ) that are invariant under multiplication by (some) functions in ; they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear...
Linearization and Connection Coefficients of Orthogonal Polynomials.
Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization...
Linearly-invariant families and generalized Meixner–Pollaczek polynomials
The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f′(z)) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f′0(z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials Pλn (x; θ,ψ) of a real variable x as coefficients of [###] where the parameters...
Lions-Peetre reiteration formulas for triples and their applications
We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted -spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability...
Local estimates for Jacobi polynomials.
Local means and wavelets in function spaces
The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type and on ℝⁿ and on ⁿ.
Local means and wavelets in function spaces with local Muckenhoupt weights
The paper deals with local means and wavelet bases in function spaces of Besov and Triebel-Lizorkin type with local Muckenhoupt weights.
Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets
We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions , where for a fixed function ϕ, denotes the one-dimensional orthogonal projection on the function , U is a group representation and g is an element of the group. They are defined as integrals , where W is an open, relatively...
Localisation fréquentielle des paquets d'ondelettes.
Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets wn suffer a lack of frequency localization. Using the L1-norm of the Fourier transform ^wn as localization criterion, they showed that the average 2-jΣn=02j-1 ||^wn||L1 blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question,...
Localization and Convergence of Eigenfunction Expansions.
Localization and summability of multiple Hermite series.
Localization of Spherical Harmonic Expansions.
L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux
Lp extremal polynomials. Results and perspectives
2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points. In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze...