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SUMMARY:1) Behavior of small cuspidal eigenpairs over degenerating sequenc
 e of finite area hyperbolic surfaces.    2) Hyperbolic derivative: classes
  and applications to composition operators
DTSTART:20131014T151500
DTEND:20131014T170000
DTSTAMP:20260609T230353Z
UID:40fe1ea15568f6099bcd26d4c07539fa1acb4c9d6e79dec4482fb34e
CATEGORIES:Conferences - Seminars
DESCRIPTION:1) Sugata Mondal (Toulouse)\n2) Shamil Makhmutov \, Sultan Qab
 oos University\, Oman\n1) Abstract: We shall talk about small cuspidal eig
 envalues of finite area hyperbolic surfaces. We shall consider a sequence 
 of finite area hyperbolic surfaces of fixed type that converges in the com
 pactification of the moduli space. We shall discuss the behavior of small 
 cuspidal eigenvpairs over this sequence. A result of D. Hejhal says that i
 f the limit of the eigenvalue sequence is strictly below 1/4 then the limi
 t is an eigenvalue of the limit surface. In fact\, one does not need the c
 uspidality 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 eig
 envalue is less than or equal to 1/4. We shall see that in this case the c
 uspidality hypothesis is necessary.\n2) Abstract: Hyperbolic function clas
 ses 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 u
 sing 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.
LOCATION:MAA110 http://plan.epfl.ch/?lang=fr&room=MA+110
STATUS:CONFIRMED
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