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math.FA2009★ 4 cited
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing…
math.FA2009
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices
Eric A. Carlen, Elliott H. Lieb
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We giv…