We give an Abelian type result relating the quasiasymptotic boundedness of tempered distributions to the asymptotics of their directional short-time Fourier transform (DSTFT). We also prove several Abelian-Tauberian results characterizing the quasiasymptotic behavior of distributions in \(\mathscr{S}'\)(ℝⁿ) in terms of their DSTFT with fixed direction.

中文翻译：

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方向性短时傅立叶变换与分布的拟症状

我们给出了一个阿贝尔类型的结果，该结果将回火分布的拟渐近有界性与其定向短时傅立叶变换（DSTFT）的渐近性相关。我们还证明几个阿贝尔-Tauberian结果在表征分布的quasiasymptotic行为\（\ mathscr {S}'\）（ℝ ^Ñ）在其与固定方向DSTFT方面。