Invariant distances and invariant differential metrics in locally convex spaces

Invariant Metrics on G-spaces

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

Locally Finitely Dimensional Shift - Invariant Spaces In

We prove that a locally nitely dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by nitely many compactly supported distributions. If the locally nitely dimensional shift-invariant space is a subspace of the HH older continuous space C or the fractional

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Projective Invariant Metrics for Einstein Spaces