Continuous inversion formulas for multi-dimensional modified Stockwell transforms

Abstract

We introduce multi-dimensional modified Stockwell transforms and give for them continuous inversion formulas, extending the work in Riba and Wong [Continuous inversion formulas for multi-dimensional Stockwell transforms. Math Model Nat Phenom. 2013;8:215–229] in different directions.

Keywords:

• Fourier transforms
• Gabor transforms
• wavelet transforms
• Stockwell transforms
• modified Stockwell transforms
• continuous inversion formulas

Mathematics Subject Classification:

• 42C40
• 47G10

Acknowledgments

The authors are grateful to the referee for the useful comments in improving the presentation of the paper.

Funding

This research was supported by grants from the Doctoral School of Sciences and Innovative Technologies, Ph.D. Program in Mathematics of Università degli Studi di Torino, and the Natural Sciences and Engineering Research Council of Canada.