# Unique continuation properties for abstract Schroedinger equations and applications

## TL;DR

This paper establishes unique continuation properties and Hardy's uncertainty principle for abstract Schrödinger equations with operator potentials in Hilbert spaces, applicable to various physical systems.

## Contribution

It generalizes unique continuation results to Schrödinger equations with operator potentials in Hilbert spaces, covering a wide range of physical models.

## Key findings

- Hardy's uncertainty principle is extended to abstract Schrödinger equations.
- Unique continuation properties are proven for equations with operator potentials.
- Applicable to numerous physical systems through appropriate space and operator choices.

## Abstract

In this paper, Hardy's uncertainty principle and unique continuation properties of Schrodinger equations with operator potentials in Hilbert space-valued classes are obtained. Since the Hilbert space H and linear operators are arbitrary, by choosing the appropriate spaces and operators we obtain numerous classes of Schrodinger type equations and its finite and infinite many systems which occur in a wide variety of physical systems.