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Synthesis Exam: Functional Analysis 🧮
Level: Master 2 Mathematics
This synthesis exam brings together the essential notions of Functional Analysis at the Master 2 level and assesses your mastery of advanced concepts. It is designed to test both your theoretical understanding and your ability to solve complex analytical problems.
🔎 Objectives
- Continuous linear functionals: Show that a function f is linear and continuous, and calculate its norm.
- Non-equivalent norms: Identify and prove that two norms on a given vector space are not equivalent.
- Completeness of the space: Verify whether this space is complete and understand its topological properties.
- Applications of the Ascoli–Arzelà theorem: Study uniform convergence and the compactness of sequences of continuous functions.
📘 Typical Content
- Theoretical exercises to consolidate advanced definitions and properties.
- Practical problems involving calculations, proofs, and applications of theorems.
- Critical analysis of sequences and transformations in normed and functional spaces.
💡 Tip: Clearly identify the assumptions and apply the properties of each concept methodically before solving a problem.
📂 Additional Resources
To prepare effectively, you can download a complete selection of solved exams in Functional Analysis (Master 2): 👉
🛒 Buy via Payhip 💳 Buy via Kooneo
🔗 Corrected Final Exam – Theory of Operator Semigroups
🔗 Continuous Assessment Test: Theory of Operator Semigroups
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