Sentence examples for be the adjoint operator from inspiring English sources

Let (tilde{mathcal{R}}= -Delta +W)^{-frac{1}{2}}nabla ) be the adjoint operator of the Riesz transform (mathcal{R}).

Let (A:H rightarrow F) be a bounded linear operator such that (Aneq 0) and let (A^) be the adjoint operator of A. Suppose that (C cap A^{-1}Dneemptyset).

Let (T E rightarrow F) be a bounded linear operator such that (Tneq 0) and let (T^) be the adjoint operator of T. Suppose that (A^{-1}0 cap T^{-1}(B^{-1}0)neemptyset).

Let (T:H rightarrow F) be a bounded linear operator such that (Tneq0) and let (T^) be the adjoint operator of T. Suppose that (A^{-1}0 cap T^{-1}(B^{-1}0) neemptyset).

Now let (A^(t):X^rightarrow X^), where (X^) is the dual of X, be the adjoint operator of (A t)in L X)), (tin I) defined by bigl(A^(t)f bigr) (x)=f bigl(A t)x bigr)quad text{for all } fin {X}^ text{ and } xin{X}.

Let (S_{i}=C_{i}times Q_{i}subseteq H=H_{1}times H_{2}), (i=1,2,ldots,t), (G=[A,-B]:Hmapsto H_{3}), (G^) be the adjoint operator of G, then the original problem (1.3) can be modified as textit{finding }w= x,y inbigcap_{i=1}^{t}S_{i} textit{ which satisfies } Gw=0.

where ({{boldsymbol {tilde w}}_{boldsymbol {t}}}) is the adjoint operator of w t, and PT T and IPT T are the adjoint operators of PT and IPT, respectively.

(4.10) where (mathcal{L}^{ast}) is the adjoint operator of the operator (mathcal{L}).

The discrete divergence operator div : Y → X is defined by div = − ∇ * (∇ * is the adjoint operator of ∇).

end{aligned} Because K is the adjoint operator, (B^{ast }=B).

where B ∗ is the adjoint operator of B. Lemma 2.1 Suppose that assumptions (A1 - A2) are satisfied.