X-rays of forms and projections of currents

Author:
Bruce Solomon

Journal:
Trans. Amer. Math. Soc. **363** (2011), 143-164

MSC (2010):
Primary 44A12, 42A85, 58A10, 58A25

Published electronically:
August 31, 2010

MathSciNet review:
2719676

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Abstract: We study a new Radon-like transform that averages projected -forms in over affine -spaces. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth -forms. Our transform differs from the one in the work by Gelfand, Graev and Shapiro (1969). Moreover, if it can be extended to a somewhat larger space of -forms, our inversion formula will allow the synthesis of any rapidly-decaying smooth -form on as a (continuous) superposition of pullbacks from -forms on -dimensional subspaces. In turn, such a synthesis implies an explicit formula (which we derive) for reconstructing compactly supported currents in (e.g., compact oriented -dimensional subvarieties) from their oriented projections onto -planes.

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Additional Information

**Bruce Solomon**

Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Email:
solomon@indiana.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-2010-05348-6

Received by editor(s):
July 22, 2008

Published electronically:
August 31, 2010

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.