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Equidistribution of cusp forms on PSL 2 ( 𝐙 ) PSL 2 ( 𝐑 )

Dmitri Jakobson (1997)

Annales de l'institut Fourier

We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on PSL 2 ( Z ) PSL 2 ( R ) . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on PSL 2 ( Z ) H .

Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds

Mikhail Shubin (1998/1999)

Séminaire Équations aux dérivées partielles

We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...

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