The spectrum of a linear operator is the infinite-dimensional generalization of the notion of eigenvalues of a matrix. In this course we discuss the basic properties of spectra of bounded and unbounded linear operators. An introduction to Banach spaces is given, and the Baire, Banach-Steinhaus, open mapping and closed graph theorems are discussed. Applications to differential equations are discussed.
Number of hours
Take-home exercises and oral or take-home examination
Metric spaces: open, closed, compact, continuity, convergence; complex variables: analyticity, contour integrals, Cauchy’s theorem; Hilbert space
This course can be part of a Leiden master programme. Please contact the lecturer shortly before the start of the 2nd semester.