The Zak transform on certain locally compact groups

Kutyniok, Gitta (2002): The Zak transform on certain locally compact groups. In: Journal of Mathematical Sciences, Bd. 1: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik