LEARNING OUTCOMES
You will learn about norms and inner products in infinite-dimensional vector spaces. Related to these structures, you will understand basic properties of bounded linear operators and duality in Hilbert spaces, together with diagonalization of compact self-adjoint operators.
Credits: 5
Schedule: 02.09.2024 - 14.10.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Ville Turunen
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Orthogonality, orthonormal bases, bounded linear operators, functionals, and elementary spectral theory in Hilbert spaces. (Jordan-von Neuman Theorem, Riesz Hilbert Space Representation Theorem, diagonalization of compact self-adjoint operators, Hilbert-Schmidt Spectral Theorem, Singular Value Decomposition).
Assessment Methods and Criteria
valid for whole curriculum period:
Weekly exercises (1/3) and an exam (2/3). Alternatively, just exam (100%).
Workload
valid for whole curriculum period:
Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca 100h.
DETAILS
Study Material
valid for whole curriculum period:
Lecture notes (additional literature to be announced at the course homepage).
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Autumn I
2025-2026 Autumn I