Functional analysis
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
D01FAN_EN | ZK | 1P+1S | English |
- Course guarantor:
- Aleš Nekvinda
- Lecturer:
- Aleš Nekvinda
- Tutor:
- Supervisor:
- Department of Mathematics
- Synopsis:
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The lectures will be devoted to the study of Hilbert and Banach spaces and operators on them with regard to applications in the theory of partial differential equations. We say basic theorems of the functional analysis, Hahn-Banach's, Banach-Steinhaus's theorem, and the theorem on open mapping and on the closed graph. The concept of dual space and reflexivity, the quadratic functional, the theorem about the minimum and the relation with the operator equation have been introduced. Furthermore, we can prove Riesz's theorem on representation and Lax-Milgram's theorem. We will introduce a weak convergence and we will prove a weak compactness of the unit ball. We show that the convex continuous coercive functional in the reflexive Banach space has a minimum. Let's mention Browder's theorem about monotone operators. Finally, we will show applications on elliptical problems.
- Requirements:
- Syllabus of lectures:
- Syllabus of tutorials:
- Study Objective:
- Study materials:
- Note:
- Time-table for winter semester 2024/2025:
- Time-table is not available yet
- Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans: