On The Approximation Of The Spectral Expansions Of Distributions In The Weak Topology.
Abdumalik A. Rakhimov · 2012
In this paper we study approximations of distributions on a smooth manifold. We obtain sufficient conditions of summation of the series in the weak topology. As applications we consider spectral expansions connected with elliptic partial differential operators. Preliminaries: Let N - dimensional manifold, i.e. a Housdorff topological space in which each point has a neighborhood, which is homeomorphic to an open N - dimensional sphere. We suppose that is a smooth manifold, which means: for each point x there exists a neighborhood x O and infinite time differentiable mapping x f of this neighborhood on a certain open set x O of the space N R and these mappings are compatible in the intersection of neighborhoods, that means if 2 1) ( x x O O then a mapping