Tauberian theorems for the Stockwell transform of Lizorkin distributions. (English) Zbl 1435.42034
In this paper, the authors prove the continuity of the Stockwell transform and its transpose, called the Stockwell synthesis operator, on the spaces of highly localized test functions over \(\mathbb{R}\) and \(\mathbb{R} \times (\mathbb{R} \setminus \{0\})\), respectively. Then using these results, they study the Stockwell transform on the space of Lizorkin distributions \(\mathcal{S}^\prime_0(\mathbb{R} )\). Also, the authors characterize the quasiasymptotic behavior of elements of \(\mathcal{S}^\prime_0(\mathbb{R} )\) in terms of abelian and Tauberian theorems for the Stockwell transform.
Reviewer: Anirudha Poria (Bengaluru)
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46F12 | Integral transforms in distribution spaces |
| 26A12 | Rate of growth of functions, orders of infinity, slowly varying functions |
| 46F10 | Operations with distributions and generalized functions |
Keywords:
Stockwell transform; distributions; quasiasymptotic behavior; Abelian and Tauberian theoremsReferences:
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