MATS2210 Hilbert-avaruudet, kevät 2026

Overview

The course Hilbert spaces takes place at the University of Jyväskylä starting on 12.01.2026 and until 15.03.2026. Please consult the official page of the course on Sisu. On this TIM page you will find all the weekly assignments and the preliminary lecture notes of the course. Please find the schedule of the lectures and other communication on this website. Should you have questions related to the lectures or the exercises, please contact me at giovanni.g.covi@jyu.fi and/or the teaching assistant at shubham.s.jaiswal@jyu.fi.

Contents

After a light introduction about metric and Banach spaces, we will study Lp spaces and the properties of linear operators, including Banach's fixed point theorem. We will then explore Hilbert spaces, discussing the concepts of orthonormality, duality, and spectrum of an operator.

Modalities of exam

Evaluation for the course can be obtained in one of the following ways:

• 100% from final - You only take part to the final exam, and your grade is the grade of the exam.

• 50% from weekly assignments, 50% from final - You solve the weekly assignments and you take part to the final exam. Your grade is the average of the two. Each problem from the assignments is given 2 points (perfect or almost perfect solution), 1 point (honest attempt) or 0 points (no solution, or very wrong solution). The grade from the assignments is obtained as percentage of points obtained over all available points.

Exercises

The exercise sessions happen on Monday afternoon. The solutions to the exercises must be given before the beginning of the session to the teaching assistant Shubham Jaiswal either in person (at lecture or in room MaD234) or by email (shubham.s.jaiswal@jyu.fi). The weekly assignments will appear here:

• Assignment 1 - Solution 1