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Original Articles

A unified extension of Stieltjes and Poisson transforms to Boehmians

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Pages 195-206 | Received 11 Apr 2010, Accepted 12 Jul 2010, Published online: 15 Jan 2011

References

  • Betancor , J. J. , Linares , M. and Méndez , J. M.R. 1995 . The Hankel transform of integrable Boehmians . Appl. Anal. , 58 : 367 – 382 .
  • Betancor , J. J. , Linares , M. and Méndez , J. M.R. 1996 . Ultraspherical transform of summable Boehmians . Math. Japon. , 44 : 81 – 88 .
  • González , B. J. and Negrin , E. R. 2009 . A distributional inversion formula for a generalization of the Stieltjes and Poisson transforms . Integral Transform. Spec. Funct. , 20 ( 12 ) : 897 – 903 .
  • Karunakaran , V. and Roopkumar , R. 2002 . Boehmians and their Hilbert transforms . Integral Transform. Spec. Funct. , 13 : 131 – 141 .
  • Karunakaran , V. and Roopkumar , R. 2002 . Ultra Boehmians and their Fourier transforms . Fract. Calc. Appl. Anal. , 5 ( 2 ) : 181 – 194 .
  • Karunakaran , V. and Roopkumar , R. 2003 . Periodic Beurling Boehmians and analytic Boehmians . Meth. Appl. Anal. , 10 ( 1 ) : 137 – 150 .
  • Mikusiński , P. 1983 . Convergence of Boehmians . Japan. J. Math. , 9 : 159 – 179 .
  • Mikusiński , P. 1987 . Fourier transform for integrable Boehmians . Rocky Mountain J. Math. , 17 : 577 – 582 .
  • Mikusiński , P. 1996 . On flexibility of Boehmians . Integral Transform. Spec. Funct. , 4 ( 1–2 ) : 141 – 146 .
  • Mikusiński , J. and Mikusiński , P. 1981 . Quotients de suites et leurs applications dans l'anlyse fonctionnelle . C. R. Acad. Sci. Paris Sér. I , 293 : 463 – 464 .
  • Mikusiński , P. , Morse , A. and Nemzer , D. 1994 . The two sided Laplace transform for Boehmians . Integral Transform. Spec. Funct. , 2 ( 3 ) : 219 – 230 .
  • Nemzer , D. 1989 . Periodic Boehmians . Int. J. Math. Math. Sci. , 12 ( 4 ) : 685 – 692 .
  • Nemzer , D. 1992 . The Laplace transform on a class of Boehmians . Bull. Austral. Math. Soc. , 46 : 347 – 352 .
  • Pettis , B. J. 1938 . On integration in vector spaces . Trans. Amer. Math. Soc. , 44 ( 2 ) : 277 – 304 .
  • Roopkumar , R. 2003 . Wavelet analysis on a Boehmian space . Int. J. Math. Math. Sci. , 2003 ( 15 ) : 917 – 926 .
  • Roopkumar , R. 2003 . On extension of Fourier transform . Int. J. Math. Game Theory Algebra , 13 : 465 – 474 .
  • Roopkumar , R. 2006 . Generalized Radon transform . Rocky Mountain J. Math. , 36 ( 4 ) : 1375 – 1390 .
  • Roopkumar , R. 2007 . Stieltjes transform for Boehmians . Integral Transform. Spec. Funct. , 18 ( 11 ) : 845 – 853 .
  • Roopkumar , R. 2009 . Mellin transform for Boehmians . Bull. Inst. Math. Acad. Sinica New Ser. , 4 ( 1 ) : 75 – 96 .
  • Roopkumar , R. 2009 . An extension of distributional wavelet transform . Colloq. Math. , 115 ( 2 ) : 195 – 206 .
  • Roopkumar , R. 2009 . Convolution theorems for wavelet transform on tempered distributions and their extensions to tempered Boehmians . Asian Eur. J. Math. , 2 ( 1 ) : 115 – 125 .
  • Roopkumar , R. 2009 . Ridgelet transform on square integrable Boehmians . Bull. Korean Math. Soc. , 46 ( 5 ) : 835 – 844 .
  • Roopkumar , R. and Negrin , E. R. 2010 . Poisson transform on Boehmians . Appl. Math. Comput. , 216 : 2740 – 2748 .
  • Zayed , A. I. and Mikusiński , P. 1995 . On the extension of the Zak transform . Methods Appl. Anal. , 2 ( 2 ) : 160 – 172 .

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