Sentence examples for limiting argument from inspiring English sources

The general case can be covered by a limiting argument.

A limiting argument allows to weaken the sign condition; however, this generalization can also be proved directly using another way based on the following lemma, see Section 4.

We may further assume, without loss of generality, − ∞ < a < b < ∞, since a uniform estimate independent of a and b will allow us a suitable limiting argument.

Combining the estimates for spheres with Poincaré's limiting argument, we deduce the corresponding results for Riesz transforms associated with the Ornstein Uhlenbeck semigroup, thus providing some extensions of P.A. Meyer's Lp inequalities.

Then begin{aligned} biglVert mathit{CWP}_{alpha }^{n} u,b,sqrt{pi } -mathit{CWP}_{alpha } -mathit{CWP}_{alphaert _{L^{infty } u,ble C_{alpha }sqrt{a} Vert f_{n}-fVert _{infty } Vert psi Vert _{1},sqrt{piigned} bigrVerte monotone convergence theorem, the limiting argument of (3.8) will be valid, and the result follows.

The student remained uncomfortable with a limiting argument that 9.99... = 10, calling it a "wildly imagined infinite growing process".

This connects their work to an older domain of mathematics with many powerful theorems that can be applied once the limiting arguments have been secured.

(c) The equality for p = 1 in both (2.2) and (2.3) is just a consequence of partial integration and limiting arguments or of straightforward modifications of the proof above.

For simplicity, in the rest of the paper, we shall often limit arguments to the choice a = 1.

Don't swear and try to limit arguments.

We estimate the resolvent of P and then prove the limit argument theorem.