Sentence examples for respective norm from inspiring English sources

X 1, X 2, and H are completion spaces of X under the respective norm.

It is shown that the space (J) of test white noise functionals has an analytic version A∞ which is an algebra as well as a topological linear space topologized by the projective limit of a sequence {Ap:pϵN} of Banach spaces with respective norm given by ∥ƒ∥Ap=supZϵCJ−p{|ƒ z)|exp[−2−1∥z∥]p2]}, where SJ−p denotes the complexification of J−p.

Thus, and are, respectively, the supremum norms on for vector and matrix functions of domains in respectively, in defined from their pointwise respective norms for each. is the n th identity matrix.

Evidently, and are Banach spaces with respective norms (1.3).

It is clear that and are Banach spaces with respective norms.

The respective norms can be defined as (lVert urVert=sup{vert u(t) vert :0leq tleq1 }) and (lVert vrVert=sup{vert v t) vert :0leq tleq1 }).

The convergence rates for q and p are (1+gamma+frac{beta}{2}) under the respective norms, which are almost close to the prediction of Theorem 4.1.

Note that P C ( J ) and P C 1 ( J ) are Banach spaces with the respective norms ∥ x ∥ ∞ = sup { | x ( t ) | : t ∈ J }, ∥ x ∥ = max { ∥ x ∥ ∞, ∥ x ′ ∥ ∞ }.

The functionals (Gamma_{1},Gamma_{4},Gamma_{3},Gamma _{4}:Yrightarrowmathbb{R}) are linear continuous with respective norms (beta_{1},bethat2},beta_{3},beta_{4}), that is, (|Gamma_{i}(x)|leqbeta_{i} Vert x Vert, |Gamma_{j} y)|leqbeta_{j} Vert y Vert,i=1,2,j=3,4).

By and,, we denote the space of continuous, real-value functions and the space of (the equivalence classes of) -integrable functions defined on endowed with the respective norms (1.3).

Put (E=C J,mathbb{R})), (J=[0,T]), and (Omega=Ecap C^{1}(J,mathbb {R})) are Banach spaces with the respective norms: Vert yVert = max_{tin J}biglvert y(t bigrvert.