JournalsprimsVol. 43 , No. 2DOI 10.2977/prims/1201011793

Estimates of Kato&#8211;Temple Type for <em>n</em>-dimensional Spectral Measures

  • S. T. Kuroda

    Tokyo, Japan
Estimates of Kato&#8211;Temple Type for <em>n</em>-dimensional Spectral Measures cover

Abstract

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.