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Ridgelet transform on square integrable Boehmians

Rajakumar Roopkumar
대한수학회 (The Korean Mathematical Society)|2009.09|대한수학회보 (Bulletin of the KMS)|제46권 제5호|pp. 835-844

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참고문헌

키워드

convolutionBoehmiansridgelet transform
주제분류수학

초록

The ridgelet transform is extended to the space of square integrable Boehmians. It is proved that the extended ridgelet transform R is consistent with the classical ridgelet transform R, linear, one-to-one, onto and both R, R^(-1) are continuous with respect to δ-convergence as well as Δ-convergence.

Abstract

The ridgelet transform is extended to the space of square integrable Boehmians. It is proved that the extended ridgelet transform R is consistent with the classical ridgelet transform R, linear, one-to-one, onto and both R, R^(-1) are continuous with respect to δ-convergence as well as Δ-convergence.

참고문헌 (16)

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  3. V. Karunakaran, "Hilbert transform for Boehmians, Integral Transforms", Spec. Funct, 9(1), pp.19~36 (2000)
  4. V. Karunakaran, "Boehmians and their Hilbert transforms", Integral Transforms Spec. Funct, 13(2), pp.131~141 (2002)
  5. V. Karunakaran, "Ultra Boehmians and their Fourier transforms", Fract. Calc. Appl. Anal, 5(2), pp.181~194 (2002)
  6. P. Mikusi´nski, "Convergence of Boehmians", Jpn. J. Math, 9(1), pp.159~179 (1983)
  7. P. Mikusi´nski, "Fourier transform for integrable Boehmians", Rocky Mountain J. Math, 17(3), pp.577~582 (1987)
  8. P. Mikusi´nski, "On flexibility of Boehmians", Integral Transforms Spec. Funct, 4(1), pp.141~146 (1996)
  9. P. Mikusi´nski, "The two-sided Laplace transform for Boehmians", Integral Transforms Spec. Funct, 2(3), pp.219~230 (1994)
  10. D. Nemzer, "The Laplace transform on a class of Boehmians", Bull. Aust. Math. Soc, 46(2), pp.347~352 (1992)
  11. R. Roopkumar, "Wavelet analysis on a Boehmian space", Int. J. Math. Math. Sci, (15), pp.917~926 (2003)
  12. R. Roopkumar, "Generalized Radon transform", Rocky Mountain J. Math, 36(4), pp.1375~1390 (2006)
  13. R. Roopkumar, "Stieltjes transform for Boehmians", Integral Transforms Spec. Funct, 18(11), pp.819~827 (2007)
  14. W. Rudin, "Real and Complex Analysis" (1987), Mc. Graw Hill Inc
  15. J. L. Starck, "The curvelet transform for image denoising", IEEE Trans. Image Process, 11(6), pp.670~684 (2002)
  16. A. I. Zayed, "On the extension of the Zak transform", Methods Appl. Anal, 2(2), pp.160~172 (1995)

관련 논문AI추천

CURVELET TRANSFORM ON RAPIDLY DECREASING FUNCTIONSR. Roopkumar, R. S. Moorthy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제2호Convolution theorems for fractional Fourier cosine and sine transforms and their extensions to BoehmiansChinnaraman Ganesan, Rajakumar Roopkumar대한수학회 · 대한수학회논문집2016 · 제31권 제4호Fourier Cosine and Sine Transformable BoehmiansChinnaraman Ganesan, Rajakumar Roopkumar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호On a class of generalized functions for some integral transform enfolding kernels of Meijer $G$ function typeShrideh Khalaf Al-Omari대한수학회 · 대한수학회논문집2018 · 제33권 제2호The Cauchy Representation of Integrable and Tempered BoehmiansDeshna Loonker, Pradeep Kumar Banerji경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제4호Boehmians on the torusDennis Nemzer대한수학회 · 대한수학회보2006 · 제43권 제4호

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