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Composite Cosine Transforms
Author(s) -
Ournycheva E.,
Rubin B.
Publication year - 2005
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000334
Subject(s) - mathematics , sine and cosine transforms , trigonometric functions , generalization , unit sphere , pure mathematics , rank (graph theory) , modified discrete cosine transform , matrix (chemical analysis) , mathematical analysis , algebra over a field , fourier transform , geometry , fractional fourier transform , fourier analysis , combinatorics , materials science , composite material
The cosine transforms of functions on the unit sphere play an important role in convex geometry, Banach space theory, stochastic geometry and other areas. Their higher‐rank generalization to Grassmann manifolds represents an interesting mathematical object useful for applications. More general integral transforms are introduced that reveal distinctive features of higher‐rank objects in full generality. These new transforms are called the composite cosine transforms , by taking into account that their kernels agree with the composite power function of the cone of positive definite symmetric matrices. It is shown that injectivity of the composite cosine transforms can be studied using standard tools of the Fourier analysis on matrix spaces. In the framework of this approach, associated generalized zeta integrals are introduced and new simple proofs given to the relevant functional relations. The technique is based on application of the higher‐rank Radon transform on matrix spaces.