Hardy type unique continuation properties for abstract Schrödinger equations and applications

Abstract

In this paper, Hardy's uncertainty principle and unique continuation properties of Schrödinger equations with operator potentials in Hilbert space-valued $L^{2}$ 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 Schrödinger type equations and its finite and infinite many systems which occur in a wide variety of physical systems.

Keywords

• schrödinger equations
• positive operators
• groups of operators
• unique continuation
• hardy's uncertainty principle