In addition, (I_{0+}^{0}) is the identical operator.
(3) Let (H((u,v),lambda)=pmlambda I u,v)+ 1-lambda JQN u,v)), where I is the identical operator.
can be extended in the usual way from the space C 0 ∞ ( D ) to an essentially self-adjoint operator on L 2 ( D ), where Δ is the Laplace operator and I is the identical operator (see Reed and Simon [2], Chapter 13).
(2) (Nunotinoperatorname{Im}L) for every (uinoperatorname{Ker}LcappartialOmega ). (3) Let (H((u,v),lambda)=pmlambda I u,v)+ 1-lambda JQN u,v)), where I is the identical operator.
If (ainmathscr{A}_{a}), then the Schrödinger operator mathit{Sch}_{a}=-Delta+a(P I=0, where Δ is the Laplace operator and I is the identical operator, can be extended in the usual way from the space (C_{0}^{infty}(D)) to an essentially self-adjoint operator on (L^{2}(D)) (see [1], Chapter 11).
If a ∈ A a, then the stationary Schrödinger operator S c h a = − Δ + a ( P ) I = 0, where Δ is the Laplace operator and I is the identical operator, can be extended in the usual way from the space C 0 ∞ ( C n to an essentially self-adjoint operator on L 2 ( C n (see [1], Ch. 13]).
If a ∈ A a, then the Schrödinger operator Sch a = − Δ + a ( P ) I = 0, where Δ is the Laplace operator and I is the identical operator, can be extended in the usual way from the space C 0 ∞ ( D ) to an essentially self-adjoint operator on L 2 ( D ) (see [[1], Ch. 11]).
If a ∈ A a, then the stationary Schrödinger operator Sch a = − Δ + a ( P ) I = 0, where Δ is the Laplace operator and I is the identical operator, can be extended in the usual way from the space C 0 ∞ ( D ) to an essentially self-adjoint operator on L 2 ( D ) (see [[1], Ch. 11]).
If a ∈ A a, then the stationary Schrödinger operator S c h a = − Δ + a ( P ) I = 0, where Δ is the Laplace operator and I is the identical operator, can be extended in the usual way from the space C 0 ∞ ( D ) to an essentially self-adjoint operator on L 2 ( D ) (see [[1], Ch. 11]).
Then, by the above arguments, we get (1) (L u,v neqlambda N u,v)), for every ((u,v in[(operatorname{dom}Lsetminus{Ker}L cappartialOmega]times 0,1)); (2) (N u,v notinoperatorname{Im}L) for every ((u,v inoperatorname{Ker}Lcap partialOmega); (3) Let (H((u,v),lambda)=pmlambda I u,v)+ 1-lambda JQN u,v)), where I is the identical operator.
