Calderon’s reproducing formula for Watson wavelet transform

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• 作者：S. K. Upadhyay ; Alok Tripathi
• 关键词：Calderon’s reproducing formula ; Watson convolution ; Watson transform ; Watson wavelet transform
• 刊名：Indian Journal of Pure and Applied Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：46
• 期：3
• 页码：269-277
• 全文大小：115 KB
• 参考文献：1.J. J. Betancor and B. J. Gonzalez, A convolution operation for a distributional Hankel transformation, Studia Mathematica, 117(1) (1985), 57-2.MathSciNet
  2.L. Debnath, Integral transforms and their applications, CRC Press, New York (1995).MATH
  3.A. Erdelyi, Higher Transcendental functions vol. 1, Mc-Graw-Hill, New York (1953).
  4.A. Erdelyi, Tables of Integral Transforms vol.1., Mc-Graw-Hill, New York (1954).
  5.E. Lieb and M. Loss, Analysis, 2nd edition, American Mathematical Society Providence Rhode Island (2001).MATH
  6.M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the study of function spaces, CBMS Regional Conference series in Mathematics, Vol. 79, American Mathematical Society, Rhode Island, (1991).MATH
  7.Roop Narain, The G-function as unsymmetrical Fourier Kernels II, Proc. Amer. Math. Soc., 14 (1963), 18-8.MATH MathSciNet
  8.R. S. Pathak and G. Pandey, Calderon’s Reproducing Formula For Hankel convolution, International Journal of Mathematics and Mathematical Sciences, 2006 (2006), 1-.MathSciNet View Article
  9.R. S. Pathak and S. Tiwari, Pseudo differential operators involving Watson transform, Appl Anal., 86(10) (2007), 1223-236.MATH MathSciNet View Article
  10.R. S. Pathak and S. Tiwari, Watson convolution operator, Prog. of Maths, 40(1&2) (2006), 57-5.MATH MathSciNet
  11.R. S. Pathak, A theorem of Hardy and Titchmarsh for Generalized Functions, Appl Anal, 18 (1984), 245-55.MATH View Article
  12.E. C. Titchmarsh, Introduction to the Theory of Fourier integrals, 2nd edition, Oxford University press, Oxford, U.K. (1948).
  13.S. K. Upadhyay and Alok Tripathi, Continuous Watson wavelet transform, Integr Transf Spec F, 23(9) (2012), 639-47.MATH MathSciNet View Article
  
• 作者单位：S. K. Upadhyay (1)
  Alok Tripathi (2)
  
  1. DST-CIMS, Department of Applied Mathematics, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221 005, India
  2. Department of Applied Mathematics, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221 005, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mathematics
  Numerical Analysis
  
• 出版者：Springer India
• ISSN：0975-7465

文摘

In this paper the inverse Watson wavelet transform is investigated, the Calderon reproducing formula of Watson convolution is obtained by generalizing the results of [6]. Some applications associated with Calderon’s reproducing formula of Watson convolution are given.