Direct integrals and spectral averaging
M. Krishna, P. Stollmann
TL;DR
This paper introduces a new method for spectral averaging of selfadjoint operators using direct integrals and the Putnam Kato theorem, providing a novel approach in spectral analysis.
Contribution
It presents a new technique leveraging the Putnam Kato theorem to prove spectral averaging results for families of selfadjoint operators.
Findings
New proof method for spectral averaging
Application of Putnam Kato theorem in spectral analysis
Enhanced understanding of direct integrals in operator theory
Abstract
A one parameter family of selfadjoint operators gives rise to a corresponding direct integral. We show how to use the Putnam Kato theorem to obtain a new method for the proof of a spectral averaging result.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Holomorphic and Operator Theory · Numerical methods in inverse problems