We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The author studies a system of polynomials orthogonal at a finite set of points its weight approximating that of the orthogonal system of classical Jacobi polynomials.
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized ...
We give a proof of the existence of a solution of reconstruction operators used in the DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency...