LF00CP21 Entire Functions (8 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Growth and zeros of entire functions, order of growth and exponent of convergence, canonical products, Hadamard factorization theorem, Phragmén-Lindelöf theorems, complex interpolation, linear fractional transformations, special functions.
Learning outcomes
After completing the course, the student will be able to
• understand why growth and zeros are among the most important properties of entire functions
• know a collection of classical results, for example, theorems by Hadamard and Phragmén-Lindelöf
• know a collection of special functions and their fundamental properties
Additional information
This course is open for everyone, including exchange students. All the course material is in English. Homework, turn-in homework and exams can be written in Finnish or in English. If there are exchange students present, the lectures will be in English, otherwise the lectures will be in Finnish.
This course can be included in the MSc advanced studies.
Lectured every two years in periods 3-4. Joensuu campus.
Description of prerequisites
Real analysis (8 cr), Series (5 cr), Integrals and function sequences (4 cr), Complex analysis a (4 cr) and Complex analysis b (4 cr).