Zeta Integrals and Integral Geometry in the Space of Rectangular Matrices
نویسنده
چکیده
f(x) det(xx)dx and the Radon transform on the space Mn,m of n × m real matrices x = (xi,j). We present a self-contained proof of the Fourier transform formula for this distribution. Our method differs from that of J. Faraut and A. Korányi [FK] in the part related to justification of the corresponding Bernstein identity. We suggest a new proof of this identity based on explicit representation of the radial part of the Cayley-Laplace operator ∆ = det(∂∂), ∂ = (∂i,j)n×m. We also study convolutions with normalized zeta distributions, and the corresponding Riesz potentials. The results are applied to investigation of Radon transforms on Mn,m.
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