Zeros of the Zak transform on locally compact abelian groups

Kaniuth, Eberhard und Kutyniok, Gitta (1998): Zeros of the Zak transform on locally compact abelian groups. In: Proceedings of the American Mathematical Society, Vol. 126: pp. 3561-3569

Abstract

Let G be a locally compact abelian group. The notion of Zak transform on L2 (Rd) extends to L2 (G). Suppose that G is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for L2 (R), we then prove that if f E L2(G) is such that its Zak transform Zf is continuous on G x G, then Zf has a zero.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0002-9939
• Language: English