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.,  bulboacamath.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. 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.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject