Sentence examples for duality space from inspiring English sources

Let E be a real Banach space and (E^) be its duality space.

If we identify H ∗ and H 0 ∗ with their dual space, then we have V ⊂ H ⊂ V ∗ and V 0 ⊂ H 0 ⊂ V 0 ∗,where V 0 ∗ is the duality space of V 0. Throughout the paper, we suppose that the following assumptions hold.

The duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space, which is identified as the local cross-sectional power.

A new type of symmetry in permutation state spaces, duality, is introduced.

By the duality of Herz spaces, we have the following corollary of Theorem 3.10.

One suppresses the natural duality of Hilbert spaces and associates the dual of (L^2_beta ) with (L^2_{-beta }) so that (psi in L^2_{-beta }) is associated with the linear functional (varphi mapsto int overline{psi (x)} varphi (x), d^nu x).

After highlighting the time-frequency duality between uniformly spaced FBMC FLO and TLO formats in Section 2, the use of the extended OFDM format is reproduced in Section 3, along with hints to some critical aspects regarding the need for oversampling and equalization.

By elucidating the duality of matter and space in the Hamiltonian formalism, we attribute asymmetry to space.

The main tools used in this paper are atomic decomposition, the orthonormal wavelet basis constructed recently by Auscher and Hytönen, the discrete Calderón-type reproducing formula, the almost orthogonal estimates, implement various stopping time arguments and the duality of the Hardy spaces with the Carleson measure spaces.

(In projective space geometry, duality holds for points and planes).

In a Hilbert space, the duality mapping is an identity mapping and for all.