Sentence examples for associated norm from inspiring English sources

for which we have the associated norm that satisfies.

Let V denote a real Hilbert space with the inner product and the associated norm ∥ ⋅ ∥.

Let the scalar inner product on (L^{2}) be denoted by ((cdot,cdot)), and the associated norm by (|cdot|).

This can be provided by defining a scalar product of two potential fields, and the associated norm.

The Euclidean inner product in (mathbb{R}^{n}) is denoted by (langle x, yrangle=x^{T}y), and the associated norm by (Vert cdot Vert ).

The scalar product in (H_{1}) is denoted by ((cdot,cdot)_{L^{2}}) and the associated norm by (vert cdot vert _{L^{2}}).

It follows that L 2 is dense in H − s and H ˜ − s with respect to the associated norms.

Using an instrument developed by the research team, 37 this study will examine the social interaction on drinking behaviour at the group level, taking into account the influence of varying social connections and associated norms and sanctions.

(Example 3.1 (revisited)) One might have the impression that regular perturbation theory is associated with norm continuity of resolvents and spectral projections and asymptotic perturbation theory always only strong convergence.

and associates norm (23).

In what follows, H denotes a complex Hilbert space with its inner product (langlecdot,cdotrangle) and its associate norm (|cdot|).