MATP25 Specialised Course in Linear Functional Analysis is an optional course for a Master of Science degree in mathematics. This course runs in parallel to the original course in Functional Analysis. Since the theory presented in those lecture is quite abstract, one objective is to exemplify those concepts and make them more accessible by means of exercises. At the same time the course offers a number of important applications of these results which cannot be presented at the level of an exercise. This part concerns for example extensions of positive linear functionals, existence of finitely additive measures on the real line (unit circle), the Toeplitz theorem on approximate identities, divergence of Fourier series, the Müntz–Szász theorem and other approximation theorems, bounded and compact integral operators, spectrum of the unilateral shift, the Voltérra operator, etc.

Teaching
The teaching consists of lectures, seminars. The student participation to both presentation of solution of exercises,
as well as presentation of more complicated results is highly encouraged
and rewarded by exam points.

Assessment
The course is assessed through a take-home examination which requires written solutions for a number of more
involved problems, due within a week.

Course literature
Peter D. Lax, Functional Analysis, (Wiley Pure and Applied Mathematics: A Series of Texts, Monographs and Tracts), 2002, ISBN: 978-0-471-55604-6.

Schedule
The schedule is available in the TimeEdit schedule tool. For instructions on how to use TimeEdit click here.

Official Course Description

MATP25-Specialised Course in Linear Functional Analysis