有理格上Schwartz Gabor标架存在的判据
Criteria for the existence of Schwartz Gabor frames over rational lattices
AI总结：
本文针对时频平面中的有理格，给出了以Schwartz类函数为窗的Gabor标架存在性的显式不等式判据，并为任意格建立了多窗Gabor标架所需窗函数个数的上界。
摘要：
我们给出了时频平面中有理格容许以Schwartz类函数为窗函数的Gabor标架的显式判据。该判据是一个不等式，用格的余体积、底层欧几里得空间的维数以及一个相关子群的指数来表述，该指数度量格的非整性程度。对于任意格，我们还给出了多窗Gabor标架所需的Schwartz类窗函数个数的上界。
英文摘要：
We give an explicit criterion for a rational lattice in the time-frequency plane to admit a Gabor frame with window in the Schwartz class. The criterion is an inequality formulated in terms of the lattice covolume, the dimension of the underlying Euclidean space, and the index of an associated subgroup measuring the degree of non-integrality of the lattice. For arbitrary lattices we also give an upper bound on the number of windows in the Schwartz class needed for a multi-window Gabor frame.
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