Sentence examples for be the associated space from inspiring English sources

Theorem 4 Let G = R or G = R +, r ∈ N, k ∈ ( 0, r ) ∖ N, E be a semi-shift invariant lattice on G that satisfy conditions (13), E 1 be the associated space to E, F be an ideal lattice such that its associated space F 1 contains the function χ ( 0, 1 ).

Theorem 3 Let G = R + or G = R, r ∈ N, k ∈ ( 0, r ) ∖ N, E be an ideal semi shift-invariant lattice on G satisfying conditions (12) and (13), and E 1 be the associated space to E. Also, let a function Ω ∈ V ( G ) be such that ( R r − k − Ω [ r − 1 ] ) ∈ E 1 and (17) hold true, for every f ∈ L ∞, E r ( G ).

Corollary 5 Let G = R or G = R +, k ∈ ( 0, 1 ), E be an ideal semi shift-invariant lattice on G satisfying conditions (12) and (13), E 1 be the associated space to E. Then, for every f ∈ L ∞, E 1 ( G ) and h > 0, the sharp inequality ∥ D − k f ∥ L ∞ ( G ) ⩽ 2 h − k Γ ( 1 − k ) ∥ f ∥ L ∞ ( G ) + ∥ τ h ∥ E 1 Γ ( 1 − k ) ∥ f ′ ∥ E (29).

Corollary 7 Let k ∈ ( 0, 1 ), E be an ideal semi shift-invariant lattice on R + satisfying conditions (12) and (13), E 1 be the associated space to E. Then, for every f ∈ L ∞, E 2 ( R + ) and h > 0, the sharp inequality ∥ D − k f ∥ L ∞ ( R + ) ⩽ 2 h − k Γ ( 2 − k ) ∥ f ∥ L ∞ ( R + ) + ∥ τ h ∥ E 1 Γ ( 2 − k ) ∥ f ″ ∥ E (32).

For any rearrangement invariant Köthe function space X on [0,+∞[, let X(M,τ) be the associated non-commutative Banach function space. This paper is concerned with ideals in M of the form IX(M,τ =M∩X(M,τ) that are contained in Lp(M,τ) for some p>0.

where (boldsymbol {Phi } : mathbf {H} rightarrow boldsymbol {mathcal {H}}) is the feature mapping indirectly defined by K, and (boldsymbol {mathcal {H}}) is the associated feature space.

Note that (Y_n) is the graph obtained by attaching a trunk of length n to Y. Let (X_n) be the metric space associated to the connected graph (Y_n), and observe that all the metric spaces (X_n) are non-amenable.

Let (lambda _{1}(Omega )be the eigenfunction space associated to (lambda _{j}(Omega )).

Let (lambda _{1}(Sigma )be the eigenfunction space associated to (lambda _{i}(Sigma )).

On the other hand, if M is bounded on the associate space (X'), then Lemma 2 shows that (7) is true.

He was the associate administrator for space science, not the NASA administrator.