Wave equations, subsidiary conditions, etc., must be expressed in terms of operators that are defined intrinsically on the cone.
In the paper [24] Daletskii and Krein proved that in the case when the self-adjoint operator A is bounded for nice functions f the map (tmapsto f(A+tK)) has m-th derivative and it can be expressed in terms a multiple operator integral whose integrand is a higher order divided difference of f.
Two sets of the ladder operators can be expressed in terms of the momentum operators as follows: begin{aligned} P_{pm } = sqrt{ 1 + nu ^2 ( P_1^2 + P_2^2 )} pm nu P_1, quad Q_{pm } = sqrt{ 1 + nu ^2 ( P_1^2 + P_2^2 )} pm nu P_2.
Inequality (20) may be expressed in the form of the operator as follows.
The MR-CISD method can be expressed in terms of the wave operator and effective Hamiltonian, and the correction is designed to modify the MR-CISD effective Hamiltonian matrix.
More generally, the dimension of the kernel and cokernel of Toeplitz or singular integral operators which and Fredholm operators can be expressed in terms of the partial indices ϰ1,…,ϰN∈Z of an associated Wiener Hopf factorization problem.
The optimal Bochner pg-frame bounds can be expressed in terms of synthesis and analysis operators.
For the special case that the entries in the Poisson and friction operators can be expressed in terms of the Dirac delta function, the strongly non-local formulation reduces to its local counterpart (see Section 2.2.2 in Öttinger 2005; Section 5 in Hütter and Tervoort 2008a).
AND and OR operators can be expressed in the conditions, by juxtaposing icons horizontally and vertically, respectively.
The Sobel operator can also be expressed in the form of two masks as shown in Figure 2: the two masks are used to calculate S y and S x, respectively.
