Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MT034	Differential Subordinates and Hardy Spaces	

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

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.	
Bibliography	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.