Abstract
In the present paper, we develop the Paley–Wiener Schwartz type theorem for Stockwell transform on compactly supported distribution spaces. Furthermore, utilizing the relationship between the Stockwell transform and the double Fourier transforms established the Paley–Wiener–Schwartz type theorem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Not applicable.
References
Stockwell, R.G., Manshinha, L., Lowe, R.P.: Localization of the complex specturm: the S transform. IEEE Trans. Signal Process. 44, 998–1001 (1996)
Guo, Q., Molahajloo, S., Wong, M.W.: Modified Stockwell Transforms and Time-Frequency Analysis. New Developments in Pseudo-differential Operators. Operator Theory: Advances and Applications, vol. 189, pp. 275–285. Birkhäuser, Basel (2009)
Catană, V.: Abelian and Tauberian results for the one-dimensional modified Stockwell transforms. Appl. Anal. 96(6), 1047–1057 (2017)
Riba, L., Wong, M.W.: Continuous inversion formulas for multi-dimensional Stockwell transforms. Math. Model. Nat. Phenom. 8(1), 215–229 (2013)
Du, J., Wong, M.W., Zhu, H.: Continuous and discrete inversion formulas for the Stockwell transform. Integr. Transforms Spec. Funct. 18(7–8), 537–543 (2007)
Liu, Y., Wong, M.W.: Inversion Formulas for Two-Dimensional Stockwell Transform. Pseudo-differential Operators, pp. 323–330. American Mathematical Society, Providence (2007)
Saneva, K.H.-V., Atanasova, S., Buralieva, V., Jasmina, T.: theorems for the Stockwell transform of Lizorkin distributions. Appl. Anal. 99(4), 596–610 (2020)
Pathak, R.S., Singh, A.: Paley–Wiener–Schwartz type theorem for the wavelet transform. Appl. Anal. 98(7), 1324–1332 (2019)
Barros-Neto, J.: An Introduction to the Theory of Distributions. Marcel Dekker, New York (1973)
Yosida, K.: Functional Analysis. Springer, Berlin (1995)
Riba, L., Wong, M.W.: Continuous inversion formulas for multi-dimensional modified Stockwell transforms. Integr. Transforms Spec. Funct. 26(1), 9–19 (2015)
Pathak, R.S.: The wavelet transform of distributions. Tohoku Math. J. (2) 56(3), 411–421 (2004)
Acknowledgements
The research of the second author is supported by University Grants Commission (UGC), Grant Number: 211610055687, New Delhi, India.
Author information
Authors and Affiliations
Contributions
All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no Conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pathak, A., Chaurasia, D.K. Paley–Wiener–Schwartz Type Theorem for the Stockwell-Transform of Distributions. Int. J. Appl. Comput. Math 10, 78 (2024). https://doi.org/10.1007/s40819-024-01707-7
Accepted:
Published:
DOI: https://doi.org/10.1007/s40819-024-01707-7