"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Univalent functions and Hardy spaces
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MT027
8
2+2+0
7.5
optional
Matematică
MT027
8
2+2+0
7.5
optional
Matematică-Informatică
Teaching Staff in Charge
Assoc.Prof. CURT Claudia Paula, Ph.D., paula@math.ubbcluj.ro
Aims
The presentation of principal classes of univalent functions.The presentation of some classic and modern results on Hardy spaces of analytic functions and some of their applications.Determination of the Hardy classes for the principal classes of univalent functions.
Content
1. Univalent functions.; basic results. Area theorem. Covering theorems (Koebe, Bieberbach). Distortion theorems (Koebe, Bieberbach). Bieberbach conjecture.
2. Analytic functions of positive real part. Harmonic functions.
3. Classes of univalent functions.
4. H^p spaces. Basic structure.
5. Applications.
6.Embedding classes of univalent functions into Hardy spaces.
References
1. P.Curt, Spatii Hardy si functii univalente,Ed. Albastra, Cluj-Napoca,2002.
2. P. Duren, Theory of H^p spaces, Acad. Press, 1970.
3. P. Duren, Univalent functions, Springer Verlag, Berlin Heidelberg, 1994.
4. G. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Mat. Soc. 1969.
5. A.W. Goodman, Univalent functions, Mariner Publishing Company Inc., 1984.
6. S.S. Miller, P.T. Mocanu, Differential Subordinations. Theory and Applications,M. Dekker,2000.
7. P.T. Mocanu, T. Bulboaca, G.St. Salagean, Teoria geometrica a functiilor univalente, Casa Cartii de Stiinta, Cluj, 1999.
8. N.Rosenblum, J.Rovnyak, Topics in Hardy Classes and Univalent Functions, Birkhauser Verlag, Basel-Boston, Berlin, 1994.
9. I. Graham, G. Kohr, Geometric function theory in one and higher dimensions,
M. Dekker, 2003.
Assessment
Exam.