The Universal Teichmüller Space and Function Space

On the Tangent Space to the Universal Teichmüller Space Subhashis Nag

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space : (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The complex-analytic model comprising 1-parameter families of schlicht functions on the exterior of the unit disc which allow quasiconformal extension. Indeed, the Fourier...

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Dynamics over Teichmüller Space

Fuzzy Subgroups and the Teichmüller Space

There exists a generalization of the Teichmüller space of a covering group. In this paper we combine this generalized Teichmüller space T (G) and any fuzzy subgroup A : G−→ F where G is a subgroup of the group consisting of such orientation preserving and orientation reversing Möbius transformations which act in the upper half-plane of the extended complex plane. A partially ordered set F = (F ...

Universal Approximator Property of the Space of Hyperbolic Tangent Functions

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.