A Taylor-like Expansion of a Commutator with a Function of Self-adjoint, Pairwise Commuting Operators
نویسنده
چکیده
LetA be a ν-vector of self-adjoint, pairwise commuting operators andB a bounded operator of classCn0 (A). We prove a Taylor-like expansion of the commutator [B, f(A)] for a large class of functions f : Rν → R, generalising the one-dimensional result where A is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.
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