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.

To study both simple and complex components of a time series, we plot

isometries as a function of the duration of the vector embedding plots, (Figures 5 and 6) [Sabelli et al.

To handle this, we first note another problem, which is that the approximate

isometries we constructed don't compose to give each other, that is

The symmetric group G(n) has a faithful representation as a group of

isometries of [R.

Any A-conection D is metrizable with respect to g if and only if all its parallel displacements are

isometries with respect to g.

Mankiewicz (30) studied the extension of

isometries defined on an open connected subset, and he proved that an isometric mapping from an open connected subset of a normed space E onto an open connected subset of another normed space F can be extended to an affine isometry from E onto F.

This has to do with the immense variety of groups of hyperbolic

isometries.

1] is adequate enough to implement the action of SO(5) via

isometries (rotations) on the internal symmetry space [S.

The group [Gamma] = [Gamma]([Omega]) then acts by

isometries on hyperbolic space.

The 37 lectures are in sections on elements of group theory, symmetry in the Euclidean world: groups of

isometries of planar and spatial objects, groups of matrices: linear algebra and symmetry in various geometries, the fundamental group: a different kind of group associated to geometric objects, from groups to geometric objects and back, and groups at large scale.

dual ball) and their distances are preserved by bijective

isometries we get by Theorem 4 a) (resp.

Among specific topics are the structure of Hopf algebras, the growth of finitely generated solvable groups, uni-modular groups over number fields,

isometries of inner product spaces, and symmetric inner product spaces over a Dedekind domain.