Are the Kramers-Kronig relations for the dielectric permittivity of a material always valid?

CONTENTS 1. Introduction 530 2. The Kramers-Kronig Relations 530 3. Consequences of the Kramers-Kronig Relations 532 4. Criteria for the Stability of a System 532 5. Stability in the Language of Macroscopic Electrodynamics 533 6. Coherent Crystallization 534 7. The Simplest Models 535 8. Applications to the Theory of Superconductivity 536 9. Conclusion 536 References 537