Operator-Theoretic Foundation of the K-Functional for Non-Normal Systems
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Abstract We develop a rigorous operator-theoretic foundation for an instability functional in non-normal linear systems. Classical spectral criteria do not control transient amplification. We introduce the K-functional K(t)=\frac{\|\Delta \mathcal{A}(t)\|}{d(\mathcal{A}(t))}\,\kappa(V)\,(1+\tau), and establish sufficient conditions for operational instability. Using semigroup theory and resolvent estimates, we connect transient growth to pseudospectral geometry and provide computable bounds and examples.
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2026-04-23
