Our aim is to generalize some results obtained for a Poisson point process in [7], to a general point process. Those results are in field of complete convergence of two like Parzen–Rosenblatt estimates of density of mean measure function and regression curves. Those estimates are defined from the superposition of n i.i.d. point processes as: where m is the number of seem generics points of the superposition. We give some sufficient conditions for the convergence of those kernel-like estimators. To cite this article: A. Diakhaby, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 597–602.相似文献
In this Note we present some results on the existence of radially symmetric solutions for the nonlinear elliptic equation
(1)
Here N?3, p>1 and denotes the Pucci's extremal operators with parameters 0<λ?Λ. The goal is to describe the solution set as function of the parameter p. We find critical exponents , that satisfy: (i) If then there is no nontrivial solution of (). (ii) If then there is a unique fast decaying solution of (). (iii) If then there is a unique pseudo-slow decaying solution to (). (iv) If pp+<p then there is a unique slow decaying solution to (). Similar results are obtained for the operator . To cite this article: P.L. Felmer, A. Quaas, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 909–914.相似文献
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804.相似文献
In the present paper, a summation formula of a general triple hypergeometric series F(3)(x, y, z) introduced by Srivastava [10] is obtained. A particular case of this formula corresponds to a result of Shah [7] involving Kampé de Fériet's double hypergeometric function which can further be specialized to yield summation formulas of Srivastava [11] and Bhatt [2] for Appell's function F2. 相似文献
Let PU(2,1) be the group of holomorphic isometries in the hyperbolic complex plane and let Gn be a sub-group of PU(2,1) which is generated by n complex reflections with respect to complex lines in . Under certain conditions, we prove that Gn is discrete. We construct representations ρ of the fundamental group Γg of the compact surface Σg of genus g, into PU(2,1), we prove they are discrete, faithful and we compute the dimension their deformation space.
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In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam. 相似文献
We construct some locally ℚp-analytic representations of GL2(L), L a finite extension of ℚp, associated to some p-adic representations of the absolute Galois group of L. We prove that the space of morphisms from these representations to the de Rham complex of Drinfel’d’s upper half space has
a structure of rank 2 admissible filtered (φ, N)-module. Finally, we prove that this filtered module is associated, via Fontaine’s theory, to the initial Galois representation. 相似文献
Nous ramenons l'existence d'estimations optimales pour la métrique de Kobayashi dans les domaines pseudoconvexes de type fini
deC2 à un principe de Bloch asymptotique. Nous établissons ce principe en combinant la méthode de renormalisation utilisée par
Gromov dans le contexte des applications harmoniques aux techniques de dilatation des coordonnées. Cecifournit une preuve
totalement élémentaire d'un résultat de Catlin particulièrement utile dans l'étude des questions de prolongement et de rigidité
d'applications holomorphes.
We solve the global Cauchy problem, with small initial data, in the space of the holomorphic functions with respect to t and Gevrey class with respect to x. We establish the existence and the stability of the solution to Cauchy problem with nul initial data without hyperbolicity hypothesis. In the stationary case, we give estimates of life span of the solutions with respect to size of the initial data. 相似文献
Let denote a strictly increasing sequence of integers; for any integer n, define A(n) to be the number of positive elements of not exceeding n. The upper and lower asymptotic densities of are defined by We describe the set of pairs (d, ), where runs over all subsequences of , as being a closed convex region of the plane. The converse statement is also proved. 相似文献
In this Note we consider a class of noncoercive nonlinear problems whose prototype is where is a bounded open subset of (N?2), △p is the so called p-Laplace operator (1<p<N) or a variant of it, μ is a Radon measure with bounded variation on or a function in , λ?0 and b belongs to the Lorentz space or to the Lebesgue space . We prove existence and uniqueness of renormalized solutions. To cite this article: M.F. Betta et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 757–762.相似文献
The aim of this work is to find a semi-global solution to the Cauchy problem (P) on a characteristic conoid C0, that is which is defined not only neighbourhood of the sumitt O, but all around the conoid parts C0 which shows the Cauchy data. In this respect, we will use the method of Kirchhoff's formulae constructed by Y. Choquet-Bruhat [4] and the results obtained from the linear case by F. Cagnac [2], Here, it is shown that all solution of (P), five times derivable, verify as such, as its derivatives up to the third order, a system of integral equations. Next this system is solved by the method of successive approximations. In this work, we do not shown that (P) has a solution. However, in a particular semilinear case (where f do not depend on the first partial derivatives), we can show that the solution of the integral system is a generalized solution of the Cauchy problem. 相似文献
Zusammenfassung Sei X eine glatte Kompaktifizierung einer zusammenhängenden linearen Gruppe über einem Körper k. Die Chowgruppe der nulldimensionalen Zyklen von X vom Grad Null ist eine Torsionsgruppe. Wir zeigen: wenn k ein p-adischer Körper ist, dann ist der prim-zu-p-Anteil dieser Gruppe endlich. 相似文献
We extend to the setting of Dirichlet series previous results of Bohr for Taylor series in one variable, themselves generalized by Paulsen, Popescu and Singh or extended to several variables by Aizenberg, Boas and Khavinson. We show in particular that, if , with , then and even slightly better, and , C being an absolute constant. To cite this article: R. Balasubramanian et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).相似文献
We study in this Note the solutions of the 2D Navier–Stokes equations with initial data in ?BMO. For in the closure of the Schwartz class, we obtain the existence and uniqueness of a global solution, and besides an estimate on its norm in ?BMO. To cite this article: P. Germain, C. R. Acad. Sci. Paris, Ser. I 340 (2005).相似文献
We prove two results on the density of states of the discrete one dimensional quasi-periodic Schrödinger equation with an analytic potential and Diophantine frequencies in the perturbed regime. On the one hand, we prove that this function has the behavior of a Hölder- function. On the other, we show that the length of the gaps has a sub-exponential estimate which depends on its label given by the gap-labeling theorem. To cite this article: S. Hadj Amor, C. R. Acad. Sci. Paris, Ser. I 343 (2006).相似文献