04-182 Vladimir Georgescu, Sylvain Golenia
Isometries, Fock Spaces, and Spectral Analysis of Schroedinger Operators on Trees (347K, PDF) Jun 9, 04
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Abstract. We construct conjugate operators for the real part of a completely non unitary isometry and we give applications to the spectral and scattering theory of a class of operators on (complete) Fock spaces, natural generalizations of the Schroedinger operators on trees. We consider C*-algebras generated by such Hamiltonians with certain types of anisotropy at infinity, we compute their quotient with respect to the ideal of compact operators, and give formulas for the essential spectrum of these Hamiltonians.

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