Segal spaces, spans, and semicategories

1.2 Segal Spaces and Complete Segal Spaces.............................. 11

1.2 Segal Spaces and Complete Segal Spaces.............................. 11

The Segal–Bargmann Transform for Odd-Dimensional Hyperbolic Spaces

We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

Compact Toeplitz operators on Segal–Bargmann type spaces

We consider Toeplitz operators with symbols enjoying a uniform radial limit on Segal–Bargmann type spaces. We show that such an operator is compact if and only if the limiting function vanishes on the unit sphere. The structure of the C∗-algebra generated by Toeplitz operators whose symbols admit continuous uniform radial limits is also analyzed.

Searching for realizations of finite metric spaces in tight spans

An important problem that commonly arises in areas such as internet trafficflow analysis, phylogenetics and electrical circuit design, is to find a representation of any given metric D on a finite set by an edge-weighted graph, such that the total edge length of the graph is minimum over all such graphs. Such a graph is called an optimal realization and finding such realizations is known to be ...