01-201 Marius Mantoiu

On a Class of Anisotropic Schrodinger Operators (491K, Postscript) May 30, 01

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Abstract. We introduce a C*-algebra containing the resolvents of a certain class of Schrodinger operators. Their potentials are anisotropic; they tend in radial directions to (different) almost periodic functions. The technique consists in defining a suitable compactification of the configuration space; a rather straightforward procedure leads then to the relevant C*-algebra. It is shown that the quotient of this C*-algebra by the ideal of compact operators has a remarcable structure. As an application, we calculate the spectrum of the affiliated anisotropic operators in terms of the spectra of a family of "asymptotic Hamiltonians".

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