Range characterization of the cosine transform on higher Grassmannians
By Semyon Alesker, J. Bernstein. 2001
67 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/82d6876aad22afa65d880862578699c6309e25b9
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In Applied Mathematics
- A. Bernig
- Franz E. Schuster
- Monika Ludwig
- Christoph Haberl
- Semyon Alesker
- Thomas Wannerer
- Joseph H. G. Fu
- Judit Abardia
In Mathematical Physics
- A. Bernig
- Franz E. Schuster
- Joseph H. G. Fu
- Christoph Haberl
- Semyon Alesker
- Thomas Wannerer
- Monika Ludwig
- Daniel Hug
Citations in the corpus
- Crofton Measures and Minkowski Valuations (2010, methodology): “Moreover, from an application of the Casselman–Wallach theorem [16] to the main result of [9], Alesker [3, p.”
- Theory of Valuations on Manifolds: A Survey (2006, methodology): “The proof of this theorem in [7] uses, besides much of the machinery of the valuation theory, the results on the Radon transform on Grassmannians due to Gelfand, Graev, Roşu [27] and the solution of the cosine transform problem for Grassmannians by Bernstein and the author [14].”
- Harmonic Analysis of Translation Invariant Valuations (2010, background): “Earlier versions of Theorem 1 for even valuations were obtained in [5] and [10].”
- Hard Lefschetz Theorem for Valuations, Complex Integral Geometry, and Unitarily Invariant Valuations (2002, methodology): “Thus it is equal to f(E) ·volE , where volE is the volume form on E defined by the metric on V , and f(E) is a constant depending on E.”
- The null space property for sparse recovery from multiple measurement vectors (2011, unknown): “The p-perimeter of parallelogram AECF is 30 which is larger than the p-perimeter 8 + 4 √ 29 of parallelogram ABCD although the parallelogram AECF is contained in the parallelogram ABCD.”
- Minkowski valuations intertwining the special linear group (2012, background): “, [1–4, 8, 11, 15, 20, 33, 36, 40, 41]), the study of valuations headed mainly in two different directions during the last years.”
- Hermitian integral geometry (2008, methodology): “This follows from the AleskerBernstein theorem [4] (compare also Section 1 in [1]).”
- Algebraic Integral Geometry (2010, methodology): “For this last statement, the Casselman-Wallach theorem is used again, compare [17].”