Book Review: Spectral theory and differential operators

Topics from spectral theory of differential operators

Introduction 2 1. Self-adjointness of Schrödinger operators 3 1.0. Solving the Schrödinger equation 3 1.1. Linear operators in Hilbert space 7 1.2. Criteria for (essential) self-adjointness 13 1.3. Application to Schrödinger operators 18 2. Hardy-Rellich inequalities 21 2.0. Relative boundedness 21 2.1. Weighted estimates 24 2.2. Explicit bounds 26 3. Spectral properties of radially periodic Sc...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

Invariant Theory and Differential Operators

Constructive invariant theory was a preoccupation of many nineteenth century mathematicians, but the topic fell out of fashion in the early twentieth century. In the latter twentieth century the topic enjoyed a resurgence, partly due to its connections with the construction of moduli spaces in algebraic geometry and partly due to the development of computational algorithms suitable for implemen...

Spectral theory of transfer operators∗

We give a survey on some recent developments in the spectral theory of transfer operators, also called Ruelle-Perron-Frobenius (RPF) operators, associated to expanding and mixing dynamical systems. Different methods for spectral study are presented. Topics include maximal eigenvalue of RPF operators, smooth invariant measures, ergodic theory for chain of markovian projections, equilibrium state...

Multidimensional Schrödinger Operators and Spectral Theory

Here we present some fundamental theorems of Schrödinger operators and their spectral theory.