Credits: 5

Schedule: 11.09.2019 - 21.10.2019

Teaching Period (valid 01.08.2018-31.07.2020): 

I Autumn (2018-2019, 2019-2020)

Learning Outcomes (valid 01.08.2018-31.07.2020): 

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.

Content (valid 01.08.2018-31.07.2020): 

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 01.08.2018-31.07.2020): 

Weekly exercises (1/3) and an exam (2/3). Alternatively, just exam (100%).

Workload (valid 01.08.2018-31.07.2020): 

Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca 100h.

Study Material (valid 01.08.2018-31.07.2020): 

Lecture notes (additional literature to be announced at the course homepage).

Substitutes for Courses (valid 01.08.2018-31.07.2020): 

MS-E1460 Functional Analysis, Mat-1.3460 Principles of Functional Analysis.

Course Homepage (valid 01.08.2018-31.07.2020): 

https://mycourses.aalto.fi/course/search.php?search=MS-E1461

Prerequisites (valid 01.08.2018-31.07.2020): 

MS-A00XX, MS-A01XX, MS-C1540

Grading Scale (valid 01.08.2018-31.07.2020): 

0-5

Further Information (valid 01.08.2018-31.07.2020): 

This course is related to MS-E1462 Banach spaces, but these two courses are not prerequisites to each other. Hilbert spaces are a special case of Banach spaces important in many applications.

Description

Registration and further information