0
votes
1answer
21 views

Pullback via flow as operator group

Let $X$ be a vector field on a manifold $M$ that induces a complete flow $\Theta_t$. Then the operator family $\Theta_t^*$, $$\Theta_t^*u(x) = u(\Theta_t(x))$$ is a strongly continuous semigroup of ...
1
vote
1answer
115 views

Laplacian on space of measures

Let $X$ be a compact Riemannian manifold and let $\mathcal{M}(X)$ be the space of regular finite Borel measures with the total variation as norm. The Laplace-Belrami-Operator $\Delta$ on $X$ with ...
2
votes
0answers
101 views

Invariant linear manifolds for multiplication by the independent variable in L^2 (R)

In general I am trying to determine when the self-adjoint operator $M$ of multiplication by the independent variable in $L^2 (\mathbb{R})$ has a symmetric restriction to a dense linear manifold ...
2
votes
2answers
232 views

Smooth dependence of the spectrum on the operator

I would like to know if there are theorems that state under which circumstances spectra of operator families depend smoothly on the parameter. To clarify, suppose I have a 1-parameter family $T_h$ of ...
13
votes
1answer
1k views

Essential self-adjointness of differential operators on compact manifolds

Let $L$ be a linear differential operator (with smooth coefficients) on a compact differentiable manifold $M$ (without boundary). Suppose $M$ is endowed with a smooth volume form (actually, a smooth ...