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COMPLEX ANALYSIS AND THE FUNK TRANSFORM

Bailey, T.N.    (Department of Mathematics University of Edinburgh James Clerk Maxwell Building The King′s Buildings Mayfield Road   ); Eastwood, M.G.    (Department of Pure Mathematics University of Adelaide   ); Gover, A.R.    (Department of Mathematics University of Auckland   ); Mason, L.J.    (Mathematical Institute  );
  • 초록

    The Funk transform is defined by integrating a function on the two-sphere over its great circles. We use complex analysis to invert this transform.


  • 주제어

    Funk .   Penrose .   Radon .   Zoll.  

  • 참고문헌 (23)

    1. N. M. J. Woodhouse, Contour integrals for the ultrahyperbolic wave equation, Proc. Roy. Soc. Lond. A438 (1992), 197?206. 
    2. Introduction to Penrose transform , M.G.Eastwood , The Penrose Transform and Analytic Cohomology in Representation Theory. Contemp. Math / v.154,pp.71-75,
    3. Twistor results for integral transforms , T.N.Bailey;M.G.Eastwood , Radon Transforms and Tomography, Contemp. Math. / v.278,pp.77-86,
    4. Some notes on the Radon transform and integral geometry , S.G.Gindikin , Monatsh. Math. / v.113,pp.23-32,
    5. Uber Flachen mit lauter geschlossenen geodatischen Linien , P.Funk , Math. Ann. / v.74,pp.278-300,
    6. Solutions of the zero rest-mass equations , R.Penrose , J. Math. Phys. / v.10,pp.38-39,
    7. Inversion for the Radon line transform in higher dimensions , G.A.J.Sparling , Trans. Roy. Soc. Lond. / v.A356,pp.3041-3086,
    8. The ultrahyperbolic differential equation with four independent variables , F.John , Duke Math. J. / v.4,pp.300-322,
    9. Complex methods in real integral geometry , M.G.Eastwood , The Sixteenth Winter School on Geometry and Physics, Srni, Suppl. Rendi. Circ. Mat. Palermo / v.46,pp.55-71,
    10. La convexite holomorphe dans l'espace analytique des cycles d'une variete algebrique , A.Andreotti;F.Norguet , Ann. Scuola Norm. Sup.Pisa / v.21,pp.31-82,
    11. An ultrahyperbolic analogue of the Robinson-Kerr theorem , V.Guillemin;S.Sternberg , Lett. Math. Phys. / v.12,pp.1-6,
    12. The solution of partial differential equations by means of definite integrals , H.Bateman , Proc. Lond. Math. Soc. / v.1,pp.451-458,
    13. Homogeneous complex manifolds and representations of semisimple Lie groups , W.Schmid , Ph.D. dissertation, University of California, Berkeley 1967, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surveys and Monographs / v.31,pp.223-286,
    14. The Radon transform on Zoll surfaces , V.Guillemin , Adv. Math. / v.22,pp.85-119,
    15. The Funk transform as a Penrose transform , T.N.Bailey;M.G.Eastwood;A.R.Gover;L.J.Mason , Math. Proc. Cambridge Philos Soc. / v.125,pp.67-81,
    16. Contour integrals for the ultrahyperbolic wave equation , N.M.J.Woodhouse , Proc. Roy. Soc. Lond. / v.A438,pp.197-206,
    17. Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten , J.Radon , Sachs. Akad. Wiss. Leipzig, Math.- Nat. Kl. / v.69,pp.262-277,
    18. Integral geometry in affine and projective spaces , I.M.Gelfand;S.G.Gindikin;M.I.Graev , Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat.;translated into English in J. Sov. Math. / v.16;18,pp.53-226;39-167,
    19. The theory of hyperfunctions on totally real subsets of a complex manifold with applications to extension problems , F.R.Harvey , Amer. J. Math. / v.91,pp.853-873,
    20. Real forms of the Radon-Penrose transform , A.D'Agnolo;C.Marastoni , Publ. Res. Inst. Math. Sci. / v.36,pp.337-383,
    21. Radon-Penrose transform for D-modules , A.D'Agnolo;P.Schapira , J. Funct. Anal. / v.139,pp.349-382,
    22. R.Penrose;W.Rindler , Spinors and Space-time / v.1,pp.,
    23. Zero-energy fields on real projective space , T.N.Bailey;M.G.Eastwood , Geom. Dedicata / v.67,pp.245-258,

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