Oktay Veliev Volgorde van de boeken

Focusing on the spectral analysis of non-self-adjoint Schrödinger operators, this book explores the spectrum and spectral singularities of periodic complex-valued potentials. It delves into the Mathieu-Schrödinger operator and the Schrödinger operator with parity-time (PT)-symmetric potentials, addressing the lack of a general spectral theorem for non-self-adjoint operators. With detailed proofs and a thorough approach, it serves as a valuable resource for graduate students in physics and mathematics, paving the way for advancements in non-Hermitian quantum mechanics and optics.

Focusing on the multidimensional Schrödinger operator with a periodic potential, this book delves into both direct and inverse problems central to perturbation theory and spectral analysis. It meticulously derives asymptotic formulas for Bloch eigenvalues and functions across dimensions, while also estimating iso-energetic surfaces in high-energy scenarios. A novel method validates the Bethe-Sommerfeld conjecture and introduces an algorithm for uniquely determining the potential from Bloch eigenvalues, with some spectral invariants expressed through Fourier coefficients of the potential.