Localization Principle of the Spectral Expansions of Distributions Connected with Schrodinger Operator

TL;DR

This paper investigates how spectral expansions of distributions associated with Schrödinger operators are localized, providing spectral decompositions, defining classes of distributions, and estimating Riesz means in Sobolev spaces.

Contribution

It introduces a framework for spectral decompositions of distributions linked to Schrödinger operators and provides new estimates for Riesz means in Sobolev spaces.

Findings

Spectral decompositions of distributions are defined.

Localization properties of spectral expansions are established.

Estimates for Riesz means in Sobolev spaces are derived.

Abstract

In this paper the localization properties of the spectral expansions of distributions related to the self adjoint extension of the Schrodinger operator are investigated. Spectral decompositions of the distributions and some classes of distributions are defined. Estimations for Riesz means of the spectral decompositions of the distributions in the norm of the Sobolev classes with negative order are obtained.