Approximation of functions of differential operators

We will discuss recent advancements in approximation of operator functions that arise in problems of mathematical physics and noncommutative geometry. Those questions reduce to finding nice bounds and representations for (semi)-norms of approximation errors. Challenges arise, in particular, from noncommutativity of a perturbation and initial unbounded operator and from noncompactness of the perturbation. Successful resolution rests on multilinear operator integration, a powerful technical method with a long history in noncommutative analysis.

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