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Mexican hat wavelet transform of generalized functions in \(\varvec{\mathcal {G}}'\) spaces

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Abstract

In this paper, we study the Mexican hat wavelet transform (MHWT) of generalized function space \(\mathcal {G}'\). The space \(\mathcal {G}'\) consists of purely entire functions with certain advance conditions developed by Howell (J. Math. Anal. Appl. 180 (1993) 79–92; 187 (1994). An inversion formula is also established.

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References

  1. Ahlfors L V, Complex Analysis (1979) (New York: McGraw-Hill Inc.)

  2. Chui C K, An Introduction to Wavelets (1992) (San Diego: Academic Press)

  3. Hirschman I I and Widder D V, The Convolution Transform (1955) (Princeton, New Jersey: Princeton University Press)

  4. Howell K B, A new theory for Fourier analysis, Part 4, J. Math. Anal. Appl. 180 (1993) 79–92

    Article  MathSciNet  Google Scholar 

  5. Howell K B, A new theory for Fourier analysis, Part 5, J. Math. Anal. Appl. 187 (1994) 567–582

    Article  MathSciNet  Google Scholar 

  6. Karunakaran V and Venugopal T, The Weierstrass transform for a class of generalized functions, J. Math. Anal. Appl. 220(2) (1998) 508–527

    Article  MathSciNet  Google Scholar 

  7. Pathak R S, The Wavelet Transform (2009) (Amsterdam, Paris: Atlantis Press, World Scientific)

  8. Pathak R S, Integral Transforms of Generalised Functions and their Applications (1997) (Amsterdam: Gordon and Breach Science Publishers)

  9. Pathak R S and Singh A, Mexican hat wavelet transform of distributions, Integral Transforms Spec. Funct. 27(6) (2016) 468–483

    Article  MathSciNet  Google Scholar 

  10. Pathak R S and Singh A, Paley–Wiener–Schwartz type theorem for the wavelet transform, Appl. Anal. 98(7) (2019) 1324–1332

  11. Zemanian A H, Generalized Integral Transformations (1996) (New York: Interscience Publishers)

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Acknowledgements

This work is supported by SERB-DST, Govt. of India, through sanction No. ECR/2017/000394. The authors are grateful to the anonymous referee for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali, 304 022, India

    Aparna Rawat & Abhishek Singh

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  1. Aparna Rawat
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  2. Abhishek Singh
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Correspondence to Abhishek Singh.

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Communicated by Sundaram Thangavelu.

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Rawat, A., Singh, A. Mexican hat wavelet transform of generalized functions in \(\varvec{\mathcal {G}}'\) spaces. Proc Math Sci 131, 31 (2021). https://doi.org/10.1007/s12044-021-00627-6

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  • DOI: https://doi.org/10.1007/s12044-021-00627-6

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