Semyanistyi's integrals and Radon transforms on matrix spaces

DOI10.1007/s00041-007-9002-0zbMath1268.42015OpenAlexW2026736110MaRDI QIDQ939088

Boris Rubin, Elena Ournycheva

Publication date: 21 August 2008

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-007-9002-0

zbMATH Keywords

Radon transformsinversion formulasmatrix spacesRiesz distributions

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

Weighted norm inequalities for $k$-plane transforms, Invariant differential operators and the range of the matrix Radon transform, Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds, Fractional integrals associated with Radon transforms, The Radon transform on the Heisenberg group and the transversal Radon transform, Reconstruction of functions on the sphere from their integrals over hyperplane sections, Strichartz's Radon transforms for mutually orthogonal affine planes and fractional integrals

Cites Work

• Bessel functions of matrix argument
• Higher-rank wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices
• Invariant differential operators and the range of the matrix Radon transform
• Smooth functions invariant under the action of a compact Lie group
• On zeta functions associated with prehomogeneous vector spaces
• The Radon transform.
• Zeta distributions associated to a representation of a Jordan algebra
• Convolution-backprojection method for the \(k\)-plane transform, and Calderón's identity for ridgelet transforms
• Radon, cosine and sine transforms on real hyperbolic space
• Inversion formulas for the spherical Radon transform and the generalized cosine transform.
• Generalizations of the Busemann-Petty problem for sections of convex bodies
• Radon inversion on Grassmannians via Gårding-Gindikin fractional integrals
• Reconstruction of functions from their integrals over \(k\)-planes
• Zeta distributions and boundary values of Poisson transforms
• Radon transform on real, complex, and quaternionic Grassmannians
• Riesz potentials and integral geometry in the space of rectangular matrices
• Singular integrals
• An Integral Formula.
• Composite Cosine Transforms
• Local zeta functions attached to the minimal spherical series for a class of symmetric spaces
• The Cayley-Laplace differential operator on the space of rectangular matrices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item