Subject: Differential Subordinates and Hardy Spaces	Code: MT034	

Semester	 Hours: C+S+L	Type	 Section	
7	2+2+0	optional	Mathematics	
7	2+2+0	optional	Mathematics-Computer Science	

Teaching Staff in Charge	Prof. BULBOACA Teodor, Ph.D., bulboaca@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. CURT, P.: Spaţii Hardy şi funcţii univalente, Editura Albastră, Cluj-Napoca, 2002.
2. DUREN, P. L. : Theory of H^p spaces, Acad. Press, 1970.
3. DUREN, P. L.: Univalent functions, Springer Verlag, Berlin Heidelberg, 1994.
4. GOLUZIN, G. M. : Geometric Theory of Functions of a Complex Variable, Trans. Math. Mon. Amer. Mat. Soc., 1969.
5. GOODMAN, A. W. : Univalent functions (vol. I, II), Mariner Publishing Co., Tampa, 1983.
6. MOCANU, PETRU - MILLER, S. SANFORD : Differential Subordinations. Theory and Applications, M. Dekker, 2000.
7. MOCANU, PETRU - BULBOACĂ, TEODOR - SĂLĂGEAN, GR. ŞTEFAN : Teoria geometrică a funcţiilor univalente, Casa Cărţii de Ştiinţă, Cluj-Napoca, 1999.
8. ROSENBLUM, N. - ROVNYAK, J. : Topics in Hardy classes and univalent functions, Birkhauser Verlag, Basel-Boston, Berlin, 1994.
9. GRAHAM, IAN - KOHR, GABRIELA : Geometric function theory in one and higher dimensions, M. Dekker, 2003.	
Assessment	Exam. Student tests during the semester; their average represents 1/3 from the final score