The Funk transform as a Penrose transform
1999 ◽
Vol 125
(1)
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pp. 67-81
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Keyword(s):
The Funk transform is the integral transform from the space of smooth even functions on the unit sphere S2⊂ℝ3 to itself defined by integration over great circles. One can regard this transform as a limit in a certain sense of the Penrose transform from [Copf ]ℙ2 to [Copf ]ℙ*ast;2. We exploit this viewpoint by developing a new proof of the bijectivity of the Funk transform which proceeds by considering the cohomology of a certain involutive (or formally integrable) structure on an intermediate space. This is the simplest example of what we hope will prove to be a general method of obtaining results in real integral geometry by means of complex holomorphic methods derived from the Penrose transform.
2019 ◽
Vol 22
(4)
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pp. 899-917
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2002 ◽
Vol 65
(1)
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pp. 55-57
2017 ◽
Vol IV-1/W1
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pp. 237-245
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2006 ◽
Vol 51
(1)
◽
pp. 51-61
1976 ◽
Vol 34
◽
pp. 538-539
1992 ◽
Vol 50
(1)
◽
pp. 694-695
2019 ◽
Vol 25
(2)
◽
pp. 256-279
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Keyword(s):
1991 ◽
Vol 30
(01)
◽
pp. 30-35
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2014 ◽
Vol 8
(5)
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pp. 931