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Energy of measures on compact Riemannian manifolds

Kathryn E. Hare, Maria Roginskaya (2003)

Studia Mathematica

We investigate the energy of measures (both positive and signed) on compact Riemannian manifolds. A formula is given relating the energy integral of a positive measure with the projections of the measure onto the eigenspaces of the Laplacian. This formula is analogous to the classical formula comparing the energy of a measure in Euclidean space with a weighted L² norm of its Fourier transform. We show that the boundedness of a modified energy integral for signed measures gives bounds on the Hausdorff...

Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories

Paulina Frej (2012)

Colloquium Mathematicae

We define the space of trajectories of a doubly stochastic operator on L¹(X,μ) as a shift space ( X ℕ , ν , σ ) , where ν is a probability measure defined as in the Ionescu-Tulcea theorem and σ is the shift transformation. We study connections between the entropy of a doubly stochastic operator and the entropy of the shift on the space of trajectories of this operator.

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