MATS2210 Hilbert Spaces (5 cr)
Description
Inner products and norms in infinite dimensional spaces, Hilbert spaces, bounded linear operators and duals, orthogonality, Fourier series, spectral decomposition of compact self-adjoint operators.
Learning outcomes
After completing the course the student:
- Masters the basic theory of Hilbert spaces.
- Has obtained skills to use Hilbert spaces in modern analysis.
Description of prerequisites
Metric Spaces, Measure and integration theory 1
Study materials
Andrew M. Bruckner, Judith B. Bruckner, and Brian S. Thomson, Real Analysis, 2008, www.classicalrealanalysis.com
Avner Friedman, Foundations of modern analysis, Dover Publications Inc. 1982; ISBN: 0-486-64062-0
Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, Wiley, 2013; ISBN: 1-118-62639-7
Lauri Kahanpää, Funktionaalianalyysi, luntomoniste 51, Matematiikan ja tilastotieteen laitos, Jyväskyän yliopisto, 2004.; ISBN: 951-39-1763-0 (in Finnish)
Lecture notes of the course
Literature
- Haïm Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2010; ISBN: 2-010-93838-2
- John B. Conway, A course in functional analysis (2nd edition), Springer, 1990; ISBN: 0-387-97245-5