一类满足Poisson型求和公式的酉算子
A Family of Unitary Operators Satisfying a Poisson-type Summation Formula
摘要：
我们考虑Poisson求和公式的一种加权形式。我们证明了在一定的衰减率条件下，存在唯一的酉Fourier-Poisson算子满足这个公式。接下来我们找到了这个算子的对角形式，并证明了在较弱的权条件下，仍然存在唯一的酉算子，它满足算子形式的Poisson求和公式。我们还将傅里叶变换和导数之间的相互作用推广到这些傅里叶-泊松算子。
英文摘要：
We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal form of this operator, and prove that under weaker conditions on the weights, a unique unitary operator still exists which satisfies a Poisson summation formula in operator form. We also generalize the interplay between the Fourier transform and derivative to those Fourier-Poisson operators.
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