Some asymptotic results for the generalized directional short-time Fourier transform

Several Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of tempered distributions in terms of their generalized directional short-time Fourier transform (DSTFT) with fixed direction, with respect to one or two variables, are proven. An Abelian-type result relating the quasiasymptotic boundedness of tempered distributions to the asymptotics of their generalized DSTFT with fixed direction is given. Also, an asymptotic result for the generalized DSTFT with fixed direction is obtained using the S-asymptotic behavior of distributions of exponential type.