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- CONTENTS
- 1986 - VOLUME 303 - SECTION I - N° 1
- Group Theory
- .......... Page(s) .......... 1
- Let D be a bounded symmetric domain, S its Shilov boundary and S (z, u) the Szegö kernel on D x S. We give the explicit Fourier series of for any positive real number . This problem was open since the classical works of Hua in the fifties.
- Mathematical Analysis
- .......... Page(s) .......... 5
- Let µ be a positive measure neglecting polar sets in Rm. We study solutions and supersolutions of the equation . These solutions are generally discontinuous but can be obtained by probabilistic or variational methods.
- .......... Page(s) .......... 7
- We consider the structure obtained as the intersection of a fixed domain with a periodic net in which the width µ of the material is small compared with the period . The material is distributed along edges (reinforced structure) or along faces (alveolar structure). The describe the global behaviour of these structures as . We prove that the limit result is independent of how (.
- Partial Differential Equations
- .......... Page(s) .......... 11
- In this Note, we extend viability theorems and equilibrium theorems for ordinary differential inclusions to partial differential inclusions of parabolic type. We then use these results for solving obstacle problems.
- Harmonic Analysis
- .......... Page(s) .......... 15
- We consider the harmonic analysis of the operator , . We prove that a maximal function closely related to the convolution structure in , is of weak type (1, 1). As a consequence, the almost everywhere convergence in various summability methods is established. We obtain also the Lp-inequalities for the g-functions g and g*, and this allow us to prove a multiplier theorem of Hörmander-Mihlin type. Finally, we study the maximal function f# and, applying a technique of Kurtz and Wheeden, we prove the weighted multiplier theorem for the Fourier-Bessel transform.
- Differential Topology
- .......... Page(s) .......... 19
- We consider the diffeotopy groups of Seifert manifolds over S2 with three exceptional fibres of order (2, 3, p) or (3, 3, q). We show that for these manifolds two homotopic diffeomorphisms are isotopic. This is done by classifying genus 2 Heegaard splittings of these manifolds.
- Probability Theory
- .......... Page(s) .......... 23
- S. T. You has proved that the Brownian motion on a complete Riemannian manifold does not explode if the Ricci curvature is bounded from below [5]. We prove an analog result in the case of a diffusion with generator , replacing the Ricci tensor R by , being the Hessian of h.
- .......... Page(s) .......... 27
- The periodic intensity of a marked point process is supposed to depend stationarily on the past. Considering successive periods, sequences of processes are defined. They are shown to be Doeblin recurrent Markov chains under specific conditions.
- We study the control of a diffusion under partial observations. We modelize the problem by enlarging the filtration of the observation and by using relaxed controls. We prove the existence of an optimal Markovian filter.
- Mathematical Physics
- This Note gives a summary of a work about semi-classical analysis of the positive part for the spectrum of Schrödinger operators:
- where V tends to zero when . We deduce the semi-classical asymptotic for the total phase shift and an estimate for the average total cross sections on energy levels without trapping classical path.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- MATHEMATIQUE 1986 - Tome 303 - Série I - n° 1
- Théorie des groupes
- .......... Page(s) .......... 1
- Analyse mathématique
- .......... Page(s) .......... 5
- Equations aux dérivées partielles
- .......... Page(s) .......... 11
- Analyse harmonique
- .......... Page(s) .......... 15
- Topologie différentielle
- .......... Page(s) .......... 19
- Probabilités
- Physique mathématique
, where µ is a measure, Denis Feyel and Arnaud de La PradelleLe taux de reconnaissance estimé pour ce document est de 93.79%.
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