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Original Articles

On the Fourier transform of distributions and differential operators in Clifford analysis

Pages 1079-1091 | Received 22 Sep 2004, Published online: 30 Aug 2006

References

References

  • Brackx F De Knock B De Schepper H Eelbode D On the fundamental solution of complex powers of the Dirac operator in Clifford analysis (submitted)
  • Brackx F Delanghe R Sommen F 1982 Clifford Analysis, Pitman Publishers Boston-London-Melbourne
  • Brackx F Delanghe R Sommen F 2004 Spherical means and distributions in Clifford analysis In: Tao Qian, Thomas Hempfling, Alan McIntosch and Frank Sommen (Eds.) Advances in Analysis and Geometry: New Developments Using Clifford Algebra, Trends in Mathematics pp. 65–96 Birkhäuser Basel
  • Brackx , F , Delanghe , R and Sommen , F . 2003 . Spherical means, distributions and convolution operators in Clifford analysis . Chinese Annals of Mathematics , 24B ( 2 ) : 133 – 146 .
  • Brackx F De Schepper H Hilbert-Dirac operators in Clifford analysis Chinese Annals of Mathematics series B (to appear)
  • Delanghe , R . 2002 . Some remarks on the principal value kernel in . Complex Variables: Theory and Application , 47 : 653 – 662 .
  • Delanghe R Sommen F Sou[cbreve]ek V 1992 Clifford Algebra and Spinor-valued Functions – A Function Theory for the Dirac Operator, Kluwer Academic Publishers Dordrecht
  • Gilbert J Murray M 1991 Clifford Algebra and Dirac Operators in Harmonic Analysis, Cambridge Univ. Press Cambridge
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  • Horváth , J . 1959 . On some composition formulas . Proc. Amer. Math. Soc. , 10 : 433 – 437 .
  • Riesz , M . 1949 . L’intégrale de Riemann-Liouville et le problème de Cauchy . Acta Math. , 81 : 1 – 223 .
  • Schwartz L 1966 Théorie des Distributions, Hermann Paris
  • Sommen , F . 1986 . Microfunctions with values in a Clifford algebra II . Sci. Pap. Coll. Art. Sci. Univ. Tokyo , 36 ( 1 ) : 15 – 37 .
  • Stein E Weiß G 1971 Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press Princeton

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