SPACES OF ANALYTIC FUNCTIONS
| Title | ΧΩΡΟΙ ΑΝΑΛΥΤΙΚΩΝ ΣΥΝΑΡΤΗΣΕΩΝ / SPACES OF ANALYTIC FUNCTIONS |
| Code | Θ022 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Petros Galanopoulos |
| Common | Yes |
| Status | Active |
| Course ID | 600025911 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268387
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268387
- eLearning:
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- Spanish
Prerequisites
General Prerequisites
General background of Complex Analysis, Functional Analysis at the level of undergraduate course
Learning Outcomes
Upon successful completion of the course students will know
1. the historical evolusion of the theory
2. to characterize the membership of an analytic function in one of the spaces under discussion
3. to evaluate the norm of these functions
4. to evaluate the norm of operators acting on the the spaces under discussion
General Competences
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
We will study the basic properties of the main spaces of analytic functions in the unit disc of the complex plane.
We will study the functions that belong to them with respect to their point-wise growth, the growth of their Taylor coefficients, the geometric properties of the image of the unit disc through them, their boundary behavior. We will study the action of important operators on the spaces under discussion
Keywords
spaces of analytic functions, unit disc of the complex plane, operators acting on spaces of analytic functions
Educational Material Types
- Notes
- Slide presentations
- Multimedia
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Description
Use of computer programs, devoted to supporting research in algebraic
geometry and commutative algebra. Online exercise hours.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 183 | ||||
| Tutorial | 13 | ||||
| Project | 20 | ||||
| Written assigments | 40 | ||||
| Exams | 5 | ||||
| Total | 300 |
Student Assessment
Description
The final grade for this course will be calculated as follows:
1. Midterm: 30%
2. Final exam: 50%.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Performance / Staging (Formative, Summative)
Bibliography
Additional bibliography for study
P. Duren Theory of Hardy spaces
J.B.Garnett Bounded Analytic functions
K.Zhu Operators on Banach spaces
Last Update
17-05-2025
