Sentence examples for this proof involves from inspiring English sources

The main difficulty in this proof involves showing that for (left| lambda -lambda _{0}right| ) sufficiently small, (Hleft( cdot,lambda right) Bleft( x;rright) rightarrow Bleft( x;rright).) We prove this step in detail, adopting the notation in the proof above.

For each non-convex domain, the proof involves the construction of an allocation rule that is not implementable.

For cubics in (2+2 -dimensions, the proof involves decomposing the operator near the conic zero variety of the determinant of the Hessian of the phase function, using an elaboration of the general approach of Phong and Stein [D.H. Phong, E.M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. (2+2 -dimensions03–722].

Proof The proof involves showing that the conditions of Theorem 5.1 hold on every strip of S θ, a and is omitted for brevity.

The remaining part of the proof is similar to that of Theorem 2.3 and so we may omit for the proof involved.

Their proof involves asymptotic analysis of an ingeniously chosen vector field, and the divergence theorem.

The method of proof involves an amalgamation of the Mackey Machine and the Orbit Method.

The proof involves a development of Lax-Phillips theory in a generalized setting, a Poisson formula for scattering poles, and some simple Tauberian arguments.

The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces.

Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators ("positive temperature Hamiltonians") which generate the dynamics of the systems under consideration.

The proof involves repeated usage of Theorems 3.6 and 3.7.