Harmonic analysis associated with the generalized differential-difference operator on the real line and quantitative uncertainty principles for its Hartley transform

Abstract

We consider a new differential-difference operator 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 the Hartley transform associated to the operator .

Keywords:

• Differential–difference operator
• Hartley transform
• quantitative uncertainty principles Donoho–Stark’s uncertainty principle
• variants of Heisenberg’s uncertainty principle

AMS Subject Classifications:

• 42A38
• Secondary: 42B10

Acknowledgements

The author gratefully acknowledges the Deanship of Scientific Research at the University of Taibah University on material and moral support. The author is deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article.

Notes

No potential conflict of interest was reported by the author.

Dedicated to Khalifa Trimèche for his 70 birthday.