Spectral theory of non-self-adjoint Dirac operators and other dispersive models

Winner of the Competition “Prize for PhD Thesis 2023” arranged by Sapienza University Press. Since the turn of the millennium, there has been growing interest in the study of non-self-adjoint operators in Quantum Mechanics, driven by both their physical relevance and mathematical challenges. The first part of this book focuses on the spectral theory of non-selfadjoint operators, particularly the Dirac operators, and the confinement of their eigenvalues within compact regions of the complex plane. The second part shifts to the study of nonlinear hyperbolic equations with time-dependent coefficients and small initial data, exploring blowup phenomena, critical exponents, and lifespan estimates.