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It is well known that the resolvent of the free Schrödinger operator on weighted L 2 spaces has norm decaying like λ - 1 2 at energy λ . There are several works proving analogous high frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions n ≥ 3 . We prove that the same estimates remain valid in all dimensions n ≥ 2 . [ABSTRACT FROM AUTHOR]

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh-Weyl m-function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries and Schrödinger operators with compactly supported potentials. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. [ABSTRACT FROM AUTHOR]