Motivated by the Backer's and Villa's results concerning (into) isometries, and Harori's work on linear extendability of surjective isometries between open subgroups of invertible elements in Banach algebras, in this paper we first investigate linear extendability of an

isometry from a certain open subset U of a Banach space X into a Banach space Y, in the case where Y is either the space [C.

The searching algorithm has the difficulty of applying 8 different

isometry transformations to the individual domain block since it operates on the entire search window using 2D FFT.

Here i denotes the sequence of the original tiling, then i' is the sequence of the tiling after applying the

isometry.

i1], the

isometry from the polar decomposition of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is invertible.

They show that if the signal is sparse under a redundant dictionary, and the combination of the dictionary and some random sampling matrix satisfies Restricted

Isometry Property (RIP) [1,3,4], then CS can still implement via the existing reconstruction algorithms, such as Basis Pursuit (BP) [12].

Werner Muller of Bale in Switzerland introduced his 'anatometric' double bundle technique in 1982 attempting to combine anatomic reconstruction principles with the concept of graft

isometry (Muller 1983) (Figure 11).

1] is similar to an invertible

isometry B (on an equivalent normed linear space) with [sigma](B) = 1 ([12], Theorem 2).

Let f be an

isometry immersion of a Riemannian manifold [M.

Hasegawa and Yamauchi [8] have proved that 1) infinitesimal holomorphically projective transformation is infinitesimal

isometry on a compact Kahlerian manifold with non-positive constant scalar curvature and 2) a compact Kahlerian manifold M with constant scalar curvature is holomorphically isometric to a complex projective space with the Fubini-Study metric if M admits a non-isometric infinitesimal holomorphically projective transformation.

Here, partial

isometry means that [parallel]Ux[parallel] = [parallel]x[parallel] for all x [member of] ker [U.

Indeed, the Kuratowski embedding is an

isometry, more precisely we have the following Lemma (see, e.

The term

Isometry was designated to define the field in which proportionality exists between EM and EF and Masculine Heterometry or Feminine Heterometry define the fields in which the predominance of EM over EF exists and vice versa, respectively.