Weighted Positivity and Other Related Results

Abstract

Most of the results in the present chapter concern the $L^2$-weighted positivity of different operators. In the case of functions taking scalar values, by this positivity we mean the inequality

$$Re\int_\Omega\langle Lu,u\rangle\Psi dx\geqslant 0,\quad \forall u \in C^\infty_0(\Omega)$$

where

$$ \Psi $$

is a weight.