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Original Articles

An extension of the radon transform to clifford analysis

Pages 243-266 | Published online: 30 Jan 2009

References

  • Brackx , F. , Delanghe , R. and Sommen , F. 1982 . Clifford Analysis , Vol. 76 , London : Pitman . Research Notes in Math
  • Bureš , J. and Souček , V. 1985 . Generalized hypercomplex analysis and its integral formulas . Complex Variables , 5 : 53 – 70 .
  • Deans , S. R. 1983 . The Radon Transform and Some of its Applications , New York : Wiley-Interscience Publ .
  • Delanghe , R. and Brackx , F. 1980 . Duality in hypercomplex function theory . J. Functional Anal , 37 : 164 – 181 .
  • Gel'fand , I. M. and Shilov , G. E. 1964 . Generalized Functions , Vol. 1 , New York, London : Academic Press .
  • Helgason , S. 1984 . Groups and Geometric Analysis, Integral Geometry. Invariant Differential Operators and Spherical Functions , Orlando : Academic Press . Pure and Applied Mathematics Series
  • Hestenes , D. and Sobczyk , G. 1984 . Clifford Algebra to Geometric Calculus , Dordrecht : Reidel Publ. Co .
  • Hochstadt , H. 1971 . The Functions of Mathematical Physics , Vol. 23 , New York : Wiley-Interscience . Pure and Applied Mathematics
  • Imaeda , K. 1981 . Solution of Maxwell's equations by means of regular functions of a biquaternion variable . Bull. Okayama Univ. Sci , 17 : 25 – 33 .
  • John , F. 1955 . Plane Waves and Spherical Means , New York : Springer .
  • Lounesto , P. 1979 . “ Spinor valued regular functions in hypercomplex analysis ” . In Thesis , Helsinki .
  • Martineau , A. 1963 . Sur les fonctionnelles analytiques et la transformation de Fourier Borel . J. d'Anal. Math , 11 : 1 – 164 .
  • Sommen , F. 1982 . Some connections between Clifford analysis and complex analysis . Complex Variable , 1 : 97 – 118 .
  • Sommen , F. 1984 . Microfunctions with values in a Clifford algebra I . Rend. Circ. Mat. Palermo II , 3 : 263 – 291 .
  • Sommen , F. 1985 . Plane waves, biregular functions and hypercomplex Fourier analysis . Rend. Circ. Mat. Palermo II , 9 : 205 – 219 .
  • Sommen , F. 1984 . Plane elliptic systems and monogenic functions in symmetric domains . Rend. Circ. Mat. Palermo II , 6 : 259 – 269 .
  • Sommen , F. 1986 . Spingroups and spherical means, Clifford algebras and their applications in mathematical physics . N A.T.O. A.S.I. Ser. C , 183 : 149 – 159 .
  • Sommen , F. 1986 . Plane wave decompositions of monogenic functions . 183 to appear
  • Stein , E. 1970 . Singular Integrals and Differentiability Properties of Functions , Princeton : Princeton University Press .
  • Stein , E. and Weiss , G. 1968 . Generalizations of the Cauchy Riemann equations and representations of the rotation group . Amer. J. Math , 90 : 163 – 196 .
  • Stein , E. and Weiss , G. 1971 . Introduction to Fourier Analysis on Euclidean Spaces , Princeton : Princeton University Press .
  • Sudbery , A. 1979 . Quaternionic analysis . Proc. Cambr. Phil. Soc , 85 : 199 – 225 .

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