Range characterization of the cosine transform on higher Grassmannians

Semyon Alesker; Joseph Bernstein

doi:10.1016/S0001-8708(03)00149-X

Range characterization of the cosine transform on higher Grassmannians

Semyon Alesker^*
, Joseph Bernstein

^*Corresponding author for this work

School of Mathematical Sciences

The University of Chicago

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). We also give a geometric interpretation of this image in terms of valuations. In addition, we discuss the non-Archimedean analogues.

Original language	English
Pages (from-to)	367-379
Number of pages	13
Journal	Advances in Mathematics
Volume	184
Issue number	2
DOIs	https://doi.org/10.1016/S0001-8708(03)00149-X
State	Published - 1 Jun 2004

Keywords

Cosine transform
Grassmannians
Radon transform

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10.1016/S0001-8708(03)00149-X

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title = "Range characterization of the cosine transform on higher Grassmannians",

abstract = "We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). We also give a geometric interpretation of this image in terms of valuations. In addition, we discuss the non-Archimedean analogues.",

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AB - We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). We also give a geometric interpretation of this image in terms of valuations. In addition, we discuss the non-Archimedean analogues.

KW - Cosine transform

KW - Grassmannians

KW - Radon transform

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Range characterization of the cosine transform on higher Grassmannians

Abstract

Keywords

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