On the Space of the Linear Homeomorphisms of a Polyhedral TV-Cell with Two Interior Vertices*.
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.
In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.
[For the entire collection see Zbl 0742.00067.]In the first part some general results on Hecke algebras are recalled; the structure constants corresponding to the standard basis are defined; in the following the example of the commuting algebra of the Gelfand- Graev representation of the general linear group is examined; here is a finite field of elements; the structure constants are explicitly determined first for the standard basis and then for a new basis obtained via a Mellin-transformation....
The foliation of a Morse form on a closed manifold is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of and . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of and . The set of the ranks of all forms defining a given foliation without minimal...