Abelian and Tauberian results for the one-dimensional modified Stockwell transforms

References

• Vladimirov VS, Drozinov Ju, Zavialov BI. Tauberian theorems for generalized functions. Dordrecht: Kluwer Academic; 1988.
   Google Scholar
• Pilipovič S, Stankovič A, Teofanov N. Wavelets and quasiasymptotics at a point. J. Approx. Theory. 1997;97:40–52.
   Web of Science ®Google Scholar
• Pilipovič S, Teofanov N. Multiresolution expansion, approximation order and quasiasymptotic behavior of tempered distributions. J. Math. Anal. Appl. 2007;331:455–471.
   Web of Science ®Google Scholar
• Vindas J, Pilipovič S. Structural theorems for quasiasymptotics of distributions at the origin. Math. Nachr. 2009;282:1584–1599.
   Web of Science ®Google Scholar
• Vindas J. Structural theorems for quasiasymptotics of distributions at infinity. Pub. Inst. Math. Beograd, N.S. 2008;84:159–174.
   Google Scholar
• Pilipovič S. Quasiasymptotics expansion and Laplace transformation. Appl. Anal. 1996;35:243–261.
   Google Scholar
• Saneva K, Aceska R, Kostadinova S. Some Abelian and Tauberian results for the short-time Fourier transform, Novi Sad. J. Math. 2013;43:81–89.
   Google Scholar
• Saneva K, Vindas J. Wavelet expansions and asymptotic behavior of distributions. J. Math. Anal. Appl. 2010;370:543–554.
   Web of Science ®Google Scholar
• Vindas J, Pilipovič S, Rakic D. Tauberian theorems for the wavelet transform. J. Fourier Anal. Appl. 2011;17:65–69.
   Web of Science ®Google Scholar
• Stockwell RG, Mansinha L, Lowe RP. Localization of the complex spectrum: the S-transform. IEEE Trans. Signal Process. 1996;44:998–1001.
   Web of Science ®Google Scholar
• Guo O, Wong MW. Modified Stockwell transforms. Memorie della Academia della Scienze di Torino, Classe di Scienze Fisiche, Matematiche e Naturali Serie V. 2008;32:3–20.
   Google Scholar
• Boggiatto P, Fernández C, Galbis A. A group representation related to the Stockwell transform. Indian. Univ. Math. J. 2009;58:2277–2296.
   Web of Science ®Google Scholar
• Brown RA, Lauzon ML, Frayne R. A general description of linear time--frequency transforms and formulation of a fast inversible transform that samples the continuous S-transform spectrum non-redundantly. IEEE Trans. Signal Process. 2010;58:281–290.
   Web of Science ®Google Scholar
• Catana V. Schatten--von Neumann norm inequalities for two-wavelet localization operators associated with β-Stockwell transform. Appl. Anal. 2012;91:503–512.
   Web of Science ®Google Scholar
• Hutníková M. On the range of Stockwell transforms. Appl. Comput. Math. 2013;219:8904–8909.
   Web of Science ®Google Scholar
• Hutníková M, Mišková A. Continuous Stockwell transforms: coherent states and localization operators. J. Math. Phys. 2015;56:073504.
   Web of Science ®Google Scholar
• Liu Y, Wong MW. Inversion formulas for two-dimensional Stockwell transforms, in Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis. Vol. 52. In: Rodino L, Schukltze BW, Wong MW editors. Fields Institute Communications; 2007. p. 323–330
   Google Scholar
• Liu Y, Mohamed A. (ℝ) boundedness and compactness of localization operators associated with the Stockwell transform. Rend. Sem. Mat. Univ. Pol. Torino. 2009;67:203–214.
   Google Scholar
• Molahajloo S, Wong MW. Square integrable group representations and localization operators for modified Stockwell transforms. Rend. Sem. Mat. Univ. Pol. Torino. 2009;67:215–227.
   Google Scholar
• Riba L. 2014. Multi-dimensional Stockwell transforms and applications [PhD Dissertation]. Torino: Università degli Studi di Torino.
   Google Scholar
• Guo O, Molahajloo S, Wong MW. Modified Stockwell transform and time–frequency analysis. In: Rodino L, Wong MW, editors. New Developments in Pseudo-Differential Operators, Operator Theory: Advances and Applications. Vol. 189. Basel: Birkhäuser; 2009. p. 275–298.
   Google Scholar
• Riba L, Wong MW. Continuous inversion formulas for multi-dimensional modified Stockwell tranforms. Integral Transforms Special Functions. 2015;26:9–19.
   Web of Science ®Google Scholar
• Gröchenig K. Foundations of time--frequency analysis. Boston (MA): App. Numer. Harmon. Anal. Birkhäuser; 2001.
   Google Scholar