1) Behavior of small cuspidal eigenpairs over degenerating sequence of finite area hyperbolic surfaces. 2) Hyperbolic derivative: classes and applications to composition operators
Event details
| Date | 14.10.2013 |
| Hour | 15:15 › 17:00 |
| Speaker |
1) Sugata Mondal (Toulouse) 2) Shamil Makhmutov , Sultan Qaboos University, Oman |
| Location | |
| Category | Conferences - Seminars |
1) Abstract: We shall talk about small cuspidal eigenvalues of finite area hyperbolic surfaces. We shall consider a sequence of finite area hyperbolic surfaces of fixed type that converges in the compactification of the moduli space. We shall discuss the behavior of small cuspidal eigenvpairs over this sequence. A result of D. Hejhal says that if the limit of the eigenvalue sequence is strictly below 1/4 then the limit is an eigenvalue of the limit surface. In fact, one does not need the cuspidality hypothesis in this case. Adapting the results of S. Wolpert and L. Ji, we shall extend this result to the case when the limit of the eigenvalue is less than or equal to 1/4. We shall see that in this case the cuspidality hypothesis is necessary.
2) Abstract: Hyperbolic function classes are subsets of the class B(D) of all analytic functions ϕ in the unit disk D such that | ϕ(z)|<1 for all z in D. They are usually defined by using the hyperbolic derivative ϕ*(z)=| ϕ’(z)|/(1-| ϕ (z)|^2). We will consider some hyperbolic classes as metric spaces and show that functions from these classes induce composition operators on the Bloch space.
2) Abstract: Hyperbolic function classes are subsets of the class B(D) of all analytic functions ϕ in the unit disk D such that | ϕ(z)|<1 for all z in D. They are usually defined by using the hyperbolic derivative ϕ*(z)=| ϕ’(z)|/(1-| ϕ (z)|^2). We will consider some hyperbolic classes as metric spaces and show that functions from these classes induce composition operators on the Bloch space.
Practical information
- General public
- Free
Organizer
- Peter Buser