In this paper,we consider the convergence and saturation problems of the following discrete type interpolation operators: where f is any bounded function on the real axis R,while U(x) is an appropriate entire function of exponential type 1 and Uσ(x)=:U(σx),we obtain some resuls similar to those in the trigonometric polynomial interpolation operators’ case[4].As a special case,our results include Dryanov's results in [5].
This paper is devoted to studying the problem of optimal recovery for Sobolev function classes W2r(R) in L2(R) by using the information of function values on denumerable points.For r≥1,we determine that the optimal sampling points are arranged equidistantly in a suitable collection of sets of sampling points and find two kinds of cardinal spline interpolation as optimal algorithms.
In this paper,by the method used in [7,9,10],we construct the heat kernels (i.e.the fundamental solutions of the heat equation) of the following spaces: the quaternion hyperbolic space Sp (1,n)/Sp(1)×Sp (n),the quaternion classical domain of type Ⅲ Sp (n,C)/Sp (n),the complex Grassmannian manifold U (m+n)/U(m)×U(n).
In this paper,we prove that on a large class of bounded contractible and noncontractible domains with piecewise smooth boundary,there is at least one positive solution to Δu+a(x)u+u(N+2)/(N-2)=0 (N≥3) with zero Dirichlet boundary condition.
The present paper discusses,from a viewpoint of homology,the nature of systems (ψ,α,σ) which induce exceptional isomorphisms Φασ of the three-dimensional linear groups over commutative rings.
In this paper,a characterization of almost periodic strongly continuous Sine operator function is given,and in a Hilbert space,it is shown that the almost periodicity of a Sine operator function implies that of the corresponding Cosine operator function.
In this paper we introduce the concept of quasinormal and subnormal operators on a Krein space and prove that every quasinormal operator is subnormal.And some conditions for an operator on a Hilbert space to be a subnormal operator in the Krein space sense are obtained.
Applying the generalized maximum principle,a Liouvilletype theorem of subharmonic functions on complete Riemannian manifolds is shown and a Liouville-type differential inequality on properly immersed complete submanifolds is given.
