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math.FA2009★ 27 cited
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…
math.SP2009
Around a Sobolev-Orlicz inequality for operators of given spectral density
Michel Rumin
We prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invari…