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

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.