On nonlinear interpolation
Thomas Kappeler, Peter Topalov
TL;DR
This paper extends the Riesz-Thorin theorem, traditionally used for linear operators, to nonlinear maps within the context of spectral analysis of Schrödinger operators, providing new tools for asymptotic analysis.
Contribution
It introduces a novel extension of the Riesz-Thorin interpolation theorem to nonlinear maps, applicable to spectral quantities of Schrödinger operators.
Findings
Extended interpolation theorem to nonlinear maps
Applied to spectral asymptotics of Schrödinger operators
Provided new analytical tools for spectral analysis
Abstract
In a case study on asymptotics of spectral quantities of Schr\"odinger operators we show how the Riesz-Thorin theorem on the interpolation of linear operators can be extended to nonlinear maps.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Mathematical Analysis and Transform Methods