The Kato–Temple estimate for an isolated eigenvalue of a selfadjoint operator is extended to spectral measures on ℝ_n_, or equivalently, a commuting set of n selfadjoint operators. The proof depends on a general variational characterization of the spectrum. In the case of normal operators this corresponds to Rayleigh bounds applied to resolvents. It is also shown that the obtained estimate has a certain invariance property under an inversion of the space.
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S. T. Kuroda, Estimates of Kato–Temple Type for <em>n</em>-dimensional Spectral Measures. Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 505–520DOI 10.2977/PRIMS/1201011793