Fourier frames

• 成果类型: Article
• 署名作者: Ortega-Cerdà, J; Seip, K
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062132
• 发表日期: 2002
• 页码: 789-806
• 关键词: sequences

摘要

We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with do Branges' theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a classical inequality of H. Landau as a consequence of Pavlov's description of Riesz bases of complex exponentials and the John-Nirenberg theorem. Finally, we discuss how to transform our description into a working condition by relating it to an approximation problem for subharmonic functions. By this approach, we determine the critical growth rate of a nondecreasing function psi such that the sequence {lambda(k)}(kis an element ofZ) defined by lambda(k) + psi(lambda(k)) = k is sampling.