AIMS Mathematics, 2021, 6(1): 378-389. doi: 10.3934/Math.2021023

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On distributional finite continuous Radon transform in certain spaces

SVKM’s NMIMS University, MPSTME, V. L. Mehta Road, Vile Parle (W), Mumbai, Maharashtra, 400056, India

The classical finite continuous Radon transform is extended to generalized functions on certain spaces. The inversion formula by the kernel method is shown in a weak distributional sense. In the concluding section, its application in Mathematical Physics is discussed.
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References

1. R. S. Pathak, Orthogonal series representations for generalized functions, J. Math. Anal. Appl., 130 (1988), 316-333.

2. J. Radon, On the determination of functions from their integrals along certain manifolds, Ber. Verh, Sachs Akad Wiss., 69 (1917), 262-277.

3. J. N. Pandey, R. S. Pathak, Eigenfunction expansion of generalized functions, Nagoya Math. J., 72 (1978), 1-25.

4. R. P. Kanwal, Generalized Functions Theory and Technique: Theory and Technique, Springer Science & Business Media, 2012.

5. R. S. Pathak, Integral Transforms of Generalized Functions and Their Applications, Routledge, 2017.

6. V. R. Lakshmi Gorty, Nitu Gupta, Finite continuous Radon transforms with applications, communicated.

7. S. R. Deans, Applications of the Radon Transform, Wiley Interscience Publications, New York, 1983.

8. L. S. Dube, On finite Hankel transformation of generalized functions, Pac. J. Math., 62 (1976), 365-378.

9. P. Daras, D. Zarpalas, D. Tzovaras, M. G. Strintzis, Efficient 3-D model search and retrieval using generalized 3-D radon transforms, IEEE T. Multimedia, 8 (2006), 101-114.

10. A. G. Katsevich, A. I. Ramm, The Radon Transform and Local Tomography, CRC press, 1996.

11. I. M. Gel'fand, N. Y. Vilenkin, Generalized Functions, Applications of Harmonic Analysis, Academic Press, 2014.

12. M. Giertz, On the expansion of certain generalized functions in series of orthogonal functions, P. Lond. Math. Soc., 3 (1964), 45-52.

13. J. Hu, S. Fomel, L. Demanet, L. Ying, A fast butterfly algorithm for generalized Radon transforms, Geophysics, 78 (2013), 41-51.

14. G. G. Walter, Expansions of distributions, T. Am. Math. Soc., 116 (1965), 492-510.

15. A. H. Zemanian, Generalized Integral Transformations, 1968.

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