Sentence examples for associates norm from inspiring English sources

and associates norm (23).

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|).

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

Let Y be a closed subspace of a separable Hilbert space X endowed with the inner product and the associated norm ∥ ⋅ ∥.

We will measure averages and variances using the standard definitions for operators on L 2, denoting with 〈 ⋅, ⋅ 〉 L 2 ( R 2 ) the L 2 ( R 2 ) scalar product and with ∥ ⋅ ∥ L 2 ( R 2 ) the associated norm.

We can define on E a new inner product and the associated norm by 〈 u, v 〉 0 = 〈 B u +, v + 〉 L 2 + 〈 u 0, v 0 〉 L 2, and ∥ u ∥ = 〈 u, u 〉 0 1 2. Therefore, Φ can be written as Φ ( u ) = 1 2 ∥ u + ∥ 2 − Ψ ( u ).