The Lieb and Nazarov Inequalities for Quaternion Linear Canonical S-Transform

Danang, Dahnial
Bahri, Mawardi
Bachtiar, Nasrullah
Toaha, Syamsuddin

Journal of the Indonesian Mathematical Society
Vol. 32 No. 1 (2026): MARCH

This research introduces the quaternion linear canonical S-transform. This transform is an extension of the linear canonical S-transform within quaternion algebra. We recall the properties and present the natural link between the quaternion linear canonical transform and the quaternion linear canonical S-transform. We exploit these properties and relation to establish the Lieb and Nazarov inequalities to the quaternion linear canonical S-transform.