Sentence examples for in its norm from inspiring English sources

Note that if a sequence on l 1 converges in its norm, then it converges componentwise.

where is the inner product in, and its norm will be denoted by.

Vector (X in R^{n}), its norm is defined as (vert X vert = sqrt{X^{T}X}).

More precisely we give an upper bound for the L∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space.

For, we say that is in if is measurable and, in which case we define its norm by (1.2).

Let denote the Banach space of all continuous functions, equipped with the norm Let for each and for each For we say that is in if is measurable and in which case we define its norm by (13).

Yusheng (2009) points out that when an institution is consistent in its cultural norms, the institution has the greatest influence on people, the institution's organizational performance is strongest, and this performance relies on individual's subjective recognition and acceptance to the institution.

In particular, we show that its norm is independent of the dimension when restricted tok-forms and we present new "Essén-type" norm inequalities related to this martingale structure.

(i) A0 is dense in A with respect to its norm || · ||; (ii) (ab)* = b*a* whenever the multiplication is defined; (iii) || y ||0= supa ∈ A, || a ||≤1|| ay || for all y ∈ A0.

The number of reactions in a group is called its norm.

For (pin [1, infty),p>N/2), let (X={L^{p}(Omega)}^{2}). Assume (W= u,v in X), and its norm is defined as (Vert WVert =Vert uVert _{p}+Vert vVert _{p}).