On the Legendre and Laplace transformations
On the Reproducing Formula of Calderon.
On the self crossing six sided figure problem.
On the spectrum of the distributional kernel related to the residue.
Orthogonal harmonic analysis of fractal measures.
Paley-Wiener-type theorem for a class of integral transforms arising from a singular Dirac system.
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
Phase Retrieval Techniques for Radar Ambiguity Problems.
Pointwise Fourier Inversion: a Wave Equation Approach.
Pointwise Fourier Inversion and Localization in ...
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
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....
Problèmes de complémentation de sons-algèbre dans l'algèbre des séries de Fourier en deux variables absolument convergentes
Proof of a Conjecture on the Supports of Wigner Distributions.
Quasihomographies in the theory of Teichmüller spaces [Book]
Regular nonlinear generalized functions and applications
Regularity and Integrability of Spherical Means.
Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³
Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = (x,φ(x)): |x| ≤ 1 and let σ be the Borel measure on Σ defined by where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from to for certain p,q. For m ≥ 6 the results are sharp except for some border points.
Restrictions of Fourier transforms to curves
Let a certain curve in We investigate inequalities of the type for 3). Our results improve improve an earlier restriction theorem of Prestini. Various generalizations are also discussed.
Schwartz Kernels on Siegel II Domains.