Harmonic analysis associated with the modified Cherednik type operator and quantitative uncertainty principles for its Hartley transform

摘要

We consider a new differential–difference operator Λ on the real line. We study the harmonic analysis associated with this operator. Next, we prove various mathematical aspects of the quantitative uncertainty principles, including Donoho–Stark’s uncertainty principle and variants of Heisenberg’s inequalities for its Hartley transform associated to the operator Λ.