Square-integrable Group Representations and Localization Operators for Modified Stockwell Transforms
نویسنده
چکیده
where φb,ξ = (2π)MξT−bDξφ, the modulation operator Mξ, the translation operator T−b and the dilation operator D 1 ξ are defined by (Mξh)(x) = e ixξh(x), (T−bh)(x) = h(x− b), (Dξh)(x) = |ξ|h(ξx), for all x in R and all measurable functions h on R. The Stockwell transform is a versatile tool first introduced in [11]. More recent results on the Stockwell transform in the contexts of applications can be found in [6, 10]. The mathematical underpinnings of Stockwell transforms are developed in [4, 5, 7, 8, 9, 13].
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