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October 10, 2025Open Access

Solutions of abstract wave equations, eigenvalues and resonances

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This analysis reveals eigenvalues and resonances in non-self-adjoint operators, suggesting insights into scattering behavior.

General representation formulas for cosine and sine operator families are established, extending classical results.
This work illustrates the behavior of wave equations influenced by eigenvalues and resonates within Banach spaces.
It introduces a framework for analyzing resonances through extensions of resolvent operators into Frechet spaces.
Applications include studying operators such as Schrödinger and nonlinear wave equations, enhancing understanding of resonance phenomena.

Latushkin et al. (2025) studied this question.

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