52 citations · 103 across the 8 of their papers we have counts for
4 papers · 1 filter
On the l^{q,p} cohomology of Carnot groups
Pierre Pansu, Michel Rumin
We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight ga…
An entropic uncertainty principle for positive operator valued measures
Michel Rumin
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures…
Balanced distribution-energy inequalities and related entropy bounds
Michel Rumin
Let be a self-adjoint operator acting over a space endowed with a partition. We give lower bounds on the energy of a mixed state from its distribution in the partition…
Spectral density and Sobolev inequalities for pure and mixed states
Michel Rumin
We prove some general Sobolev-type and related inequalities for positive operators A of given ultracontractive spectral decay, without assuming e^{-tA} is submarkovian. These inequ…