Subject: Univalent Functions and Hardy Spaces	Code: MT027	

Semester	 Hours: C+S+L	Type	 Section	
8	2+2+0	optional	Mathematics	
8	2+2+0	optional	Mathematics-Computer Science	

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	
Selective 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.S. SALAGEAN, Teoria geometrica a functiilor univalente, Casa Cartii de Stiinta, Cluj, 1999.
8. N.ROSEMBLUM, 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 (70%) + student activity (30%)