Opérateurs différentiels d'ordre infini dans des espaces de fonctions entières
Opérateurs intégraux de Fourier sans phases
Oscillatory integrals with polynomial phase.
Perturbations singulières et noyaux de Poisson
Plane waves, biregular functions and hypercomplex Fourier analysis
Pointwise Fourier Inversion and Localization in ...
Polynomial approximation to integral transforms
Power Bounded Matrices of Fourier-Stieltjes Transforms.
Principe d’Heisenberg et fonctions positives
On décrit un problème naturel concernant la transformation de Fourier. Soient , deux fonctions associées par celle-ci, positives pour et nulles en zéro. Quelle est la borne inférieure pour ? En dimension supérieure, même question, l’intervalle étant remplacé par la boule de rayon . On montre l’existence d’une borne inférieure strictement positive, qui est estimée en fonction de la dimension. La dernière section montre que cette question est naturellement liée à la théorie des fonctions zêta....
Principe d'incertitude, bases hilbertiennes et algèbres d'opérateurs
Properties of certain improper integrals
Quadrature Formulas for Oscillatory Integral Transforms.
Radiation transfer in an absorbing layer bounded by a specular reflector
Rajchman measures on compact groups.
Reconstruction of functions from their triple correlations.
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Regularity of Refinable Functions Vectors.
Remark on Fourier-Stieltjes transforms of continuous measures
Remarks on Weil’s quadratic functional in the theory of prime numbers, I
This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis is true. We prove that this quadratic functional attains its minimum in the unit ball of the -space of functions with support in a given interval , and prove again Yoshida’s theorem that it is positive definite if is sufficiently small. The Fourier transform of the functional gives rise to a quadratic...
Remarques sur la formule sommatoire de Poisson
It is well known that the condition “f ∈ L¹ and f̂ ∈ L¹” is not sufficient to ensure the validity of the Poisson summation formula ∑f(k) = ∑f̂(k). We discuss here a stronger condition " and " and see for which values of a and b the condition is sufficient.