All Questions

Let $E$ and $F$ be two vector bundles over manifold $X$. Let $P:\Gamma(E)\to \Gamma(F)$ be a self-adjoint differential operator over $X$. Define inner product on the spaces $\Gamma(E)$ of smooth ...

Let $D$ be the Dirac operator acting on a spinor bundle $S$ over a complete Riemannian manifold $M$. Then $D$ is an essentially self-adjoint operator on $L^2(S)$. Suppose there is a compact subset $K\...

Let $M$ be a non-compact manifold and $D$ a first-order self-adjoint elliptic differential operator on $M$. Then is the bounded operator $$A:=\sqrt{(D^2+1)^{-1}}:L^2(M)\rightarrow H^1(M)$$ a ...