Spectral theory of non-self-adjoint Dirac operators and other dispersive modelsSapienza Università Editrice, 31 mar 2025 - 210 pagine 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. |
Parole e frasi comuni
Anal assumptions behavior Birman-Schwinger operator Birman-Schwinger principle blow-up results C₁ Cauchy problem CN×N conjecture critical exponent Cuenin damped wave equation defined Dirac matrices Dirac operator Dm,v dxdt eigenvalues exists a constant Fanelli Fourier global heat equation heat-like hence Hölder's inequality Ikeda initial data JIRn Kato-type lemma Krejčiřík Lemma lifespan estimates mass term massless Math Mathematical N. M. Schiavone non-self-adjoint Dirac nonlinear norm obtain op(Dm,v operator norm Palmieri Partial Differential Equations pcrit PF(n point spectrum positive constant potential proof of Theorem prove ps(n RA(ii recalling region Remark resolvent estimates satisfying scale-invariant damping Schrödinger operator semilinear wave equations space dimensions spectral Spectral theory Takamura test function Theorem 1.1 tm+1 Tricomi equations Wakasa Wakasugi wave-like Yagdjian ίε μ₁ Τε