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This page lists the top ten most read articles for this journal based on the number of full text views and downloads recorded on Cambridge Core over the last 30 days. This list is updated on a daily basis.
Trace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then 
for any positive integer k.
This note concerns Fourier transforms on the real positive line. In particular, we seek conditions on a real function u(x) in x > 0, that ensure that its Fourier-cosine transform v(t) = 
u(x) cos xt dx is positive. We prove first that this is so for all t > 0, if u"(x) > 0 for all x > 0, that is, that everywhere-convex functions have everywhere-positive Fourier-cosine transforms. We then obtain a complex-plane criterion for some types of non-convex u(x). Finally we consider criteria on u(x) that imply positivity of v(t) for t > t0, for some t0 > 0.