Directional Short-Time Fourier Transform and Quasiasymptotics of Distributions

Аннотация

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.