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Kaniuth, Eberhard und Kutyniok, Gitta ORCID logoORCID: https://orcid.org/0000-0001-9738-2487 (1998): Zeros of the Zak transform on locally compact abelian groups. In: Proceedings of the American Mathematical Society, Bd. 126: S. 3561-3569

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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.

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