The Zak transform on certain locally compact groups

Kutyniok, Gitta (2002): The Zak transform on certain locally compact groups. In: Journal of Mathematical Sciences, Vol. 1: pp. 62-85

Abstract

For a class of locally compact groups, which includes all connected and simply connected 2-step nilpotent Lie groups whose Lie algebra admits a basis with respect to which the structure constants are rational, we introduce a definition of the Zak transform. We prove that this Zak transform is quasi-periodic. Further, we show that it is a Hilbert space isomorphism when the range functions are restricted to a fundamental domain. Finally, we study several examples of locally compact groups with respect to properties of their Zak transform.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics