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Journal of Shanghai University >

2012 , Vol. 18 >Issue 6: 601 - 605

DOI: https://doi.org/10.3969/j.issn.1007-2861.2012.06.010

Mathematics.Physics and Chemistry

p-Cosine Transform and Its Application in Convex Geometry

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  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2012-02-10

  Online published: 2012-12-28

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Abstract

Spherical integral transformations are indispensable tools in integral geometry and convex geometry. This paper gives a direct proof to the injectivity of p-cosine transformation forp=2k+1, k∈N. Using the injectivity properties of p-cosine transformation, an important result of uniqueness of star body is obtainted, i.e., a star body is uniquely determined by its p-centroid body forp=2k+1, k∈N

Key words：  star body; dual mixed volume; p-centroid body;p-cosine transform; spherical harmonic

Cite this article

GUO Lu-jun . p-Cosine Transform and Its Application in Convex Geometry[J]. Journal of Shanghai University, 2012 , 18(6) : 601 -605 . DOI: 10.3969/j.issn.1007-2861.2012.06.010

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