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1.
We obtain new Cauchy and Poisson integral formulas for polyanalytic functions. As an application, we establish mean value theorems for polyanalytic and real polyharmonic functions in a disk. We also give applications to sharp estimates of generalized maximum modulus principle type for associated functions, and, in particular, to estimates for rational functions (components) in the problem of singularity separation for polyrational functions.  相似文献   

2.
We prove time decay estimates for several kinetic equations like the free lkansport, Boltzmann and Vlasov—Poisson Equations. We also consider solutions with infinite energy of the Vlasov—Poisson Equation and we show that low moments in the velocity variable are propagated. As a consequence, we prove that the potential energy becomes finite immediately and that the kinetic energy is locally finite. Our approach is based on new dispersive identities for transport equations.  相似文献   

3.
We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol’ski?-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.  相似文献   

4.
We consider robustness for estimation of parametric inhomogeneous Poisson point processes. We propose an influence functional to measure the effect of contamination on estimates. We also propose an M-estimator as an alternative to maximum likelihood estimator, show its consistency and asymptotic normality.  相似文献   

5.
Journal of Theoretical Probability - We show how Hölder estimates for Feller semigroups can be used to obtain regularity results for solutions to the Poisson equation $$Af=g$$ associated with...  相似文献   

6.
Doklady Mathematics - We establish two-sided estimates for the proximity, as $$t \to \infty $$ , of the Poisson integral representing the solution of the Cauchy problem for the heat equation to...  相似文献   

7.
We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-differential operator with Wentzell boundary conditions.  相似文献   

8.
We construct a semiclassical parametrix for the resolvent of the Laplacian acting on functions on nontrapping conformally compact manifolds with variable sectional curvature at infinity. We apply this parametrix to analyze the Schwartz kernel of the semiclassical resolvent and Poisson operator and to show that the semiclassical scattering matrix is a semiclassical Fourier Integral Operator of appropriate class that quantizes the scattering relation. We also obtain high energy estimates for the resolvent and show existence of resonance free strips of arbitrary height away from the imaginary axis. We then use the results of Datchev and Vasy on gluing semiclassical resolvent estimates to obtain semiclassical resolvent estimates on certain conformally compact manifolds with hyperbolic trapping.  相似文献   

9.
We are studying the existence and weak stability of a Vlasov–Poisson syste with two typs of particles , in which the electrons are supposed to be at thermal equilibrium. This modifies the source term in the Poisson equaitonm\, and estimates in the Marcinkiewicz space M3 for the potential are used to get the strong compactness of approximations using a new regularized kernal which preservs an approriate energy inequality.  相似文献   

10.
In this paper, we consider the quasi-neutral limit of the full Euler–Poisson system in one-dimensional space when the Debye length tends to zero. Due to the observation that the full Euler–Poisson system is Friedrich symmetrizable, we can obtain uniform estimates by applying the pseudo-differential energy estimates. It is shown that for well-prepared initial data the strong solution of the full Euler–Poisson system converges strongly to the compressible Euler equations in small time interval.  相似文献   

11.
We consider an algebraic method for reconstruction of a function satisfying the Poisson equation with a polynomial right-hand side in the unit disk. The given data, besides the right-hand side, is assumed to be in the form of a finite number of values of Radon projections of the unknown function. We first homogenize the problem by finding a polynomial which satisfies the given Poisson equation. This leads to an interpolation problem for a harmonic function, which we solve in the space of harmonic polynomials using a previously established method. For the special case where the Radon projections are taken along chords that form a regular convex polygon, we extend the error estimates from the harmonic case to this Poisson problem. Finally we give some numerical examples.  相似文献   

12.
We consider compound Poisson approximations of sums of integer-valued random variables and show how, repeatedly applying Stein's equation, pseudomoments can be replaced by estimates in total variation.  相似文献   

13.
We obtain estimates for derivatives of the Poisson kernels for the second order differential operators on homogeneous manifolds of negative curvature both in the coercive and noncoercive case. Received: 20 April 2001 / in final form: 18 August 2001 / Published online: 4 April 2002  相似文献   

14.
We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations.We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities.  相似文献   

15.
We derive an approximation for stop-loss premiums for a number of specific cases. Both exponential and subexponential estimates are derived while special emphasis is given to the compound Poisson case. The full set of examples should provide a wide variety of situations covering most cases occurring in practice.  相似文献   

16.
In this paper we consider a boundary-value problem for the Poisson equation with a boundary condition comprising the fractional derivative in time and the right-hand sides dependent on time. We prove the one-valued solvability of this problem, and provide the coercive estimates of the solution.  相似文献   

17.
We give an overview of the Stein-Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other applications it suffices to show the existence of couplings with certain monotonicity properties.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.  相似文献   

18.
We consider a model homogenization problem for the Poisson equation in a domain with a rapidly oscillating boundary which is a small random perturbation of a fixed hypersurface. A Fourier boundary condition with random coefficients is imposed on the oscillating boundary. We derive the effective boundary condition, prove a convergence result, and establish error estimates.  相似文献   

19.
We consider a linear elastic plate with stress-free boundary conditions and zero Poisson coefficient. We prove that under a local change of Young's modulus infinitely many eigenvalues arise in the essential spectrum which accumulate at a positive threshold. We give estimates on the accumulation rate and on the asymptotical behaviour of the eigenvalues.  相似文献   

20.
Sharp Growth Estimates for Modified Poisson Integrals in a Half Space   总被引:1,自引:0,他引:1  
Siegel  David  Talvila  Erik 《Potential Analysis》2001,15(4):333-360
For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in Rn. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems.  相似文献   

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