Sentence examples for condition for the norm from inspiring English sources

We give a sufficient condition for the norm being less than a given number.

As a convergence we find best conditions for the norm convergence of the Bochner-Riesz means on the spaces L1(G) and C G).

Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.

In this paper, we prove a Cohen type inequality for the Fourier expansion in terms of the orthogonal polynomials Necessary conditions for the norm convergence of such a Fourier expansion are given.

Hans Kelsen holds that what is normally counted as the content of a legal duty is in reality only part of a triggering condition for the mandatory norm which commands or authorizes officials to impose a sanction: "[A] norm: 'You shall not murder' is superfluous, if a norm is valid: 'He who murders ought to be punished'"(Kelsen 1967, 55).

We first give sufficient conditions for the H∞ norm being less than a given number.

Rassias [3] attempted to weaken the condition for the bound of the norm of the Cauchy difference as follows: (1.1).

In particular, Rassias [4] improved the condition for the bound of the norm of the Cauchy difference (f(x+y -f(x+y -f)).

In particular, Rassias [4] relaxed the condition for the bound of the norm of Cauchy difference (f(x+y -f(x+y -f)).

In this section we present some test examples to show that the stability of the iteration method is a coefficient condition for the convergence in the norm of to the solution of (1.4).

We give necessary and sufficient conditions for the operator-norm convergence of Trotter-type product formulae.