Strict positive definiteness on spheres via disk polynomials.
Strong asymptotics for extremal polynomials off a complex curve.
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series
The martingale Hardy space and the classical Hardy space are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from to (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a...
Strong summability of Ciesielski-Fourier series
A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).
Subspace Weyl-Heisenberg Frames.
Subsystems of the Schauder system whose orthonormalizations are Schauder bases for
Sucesiones de polinomios ortogonales estrictamente γ-típicas.
Sufficient conditions for functions to form Riesz bases in and applications to nonlinear boundary-value problems.
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
Summability and integrability of Vilenkin series.
Summability estimates of double Vilenkin-Fourier series.
Summation of Fourier series.
Sur la décomposition quadratique d'une suite de polynômes orthogonaux - II
Sur le diamètre transfini entier d'un intervalle réel
En utilisant à la fois la théorie des polynômes orthogonaux et des arguments élémentaires de géométrie des nombres, nous donnons ici des nouveaux encadrements pour le diamètre transfini entier d’un intervalle d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de et des dénominateurs de ses extrémités.
Sur les séries dont le terme général dépend de deux angles et qui servent à exprimer des fonctions arbitraires entre des limites données.
Sur l'existence des analyses multi-résolutions en théorie des ondelettes.
On montre qu'une base d'ondelettes (ψj,k) de L2(R) avec une fonction mère ψ höldérienne à support compact provient nécessairement d'une analyse multi-résolution. La fonction-père φ a alors la même régularité que la fonction ψ et peut être choisie à support compact.
Sur une perturbation de la récurrence vérifiée par une suite de polynômes orthogonaux
The Affine Frame in -adic Analysis
In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of -adic number, hence provide new mathematic tools for application of -adic analysis.
The analytic theory of matrix orthogonal polynomials.