MM514: Hilbert- and Banach Spaces (5 ECTS)

STADS: 13014301

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: dkyed@imada.sdu.dk

Additional teachers
szymanski@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM815.

Prerequisites:
None

Academic preconditions:
The content of MM517 Measure and Integration Theory is assumed to be known.

Course introduction
To introduce Functional Analysis with special emphasis on Hilbert- and Banach Space Theory. This gives the basics for more advanced studies in modern Functional Analysis, in particular in Operator Algebra Theory and Banach Space Theory.

Expected learning outcome
By the end of the course the student will be able to:

• give an oral presentation of the statement and proofs related to any subject on a previously given list of topics within the course syllabus
• formulate the oral presentation in a mathematically correct way
• compute Fourier series and Fourier integrals of standard functions
• answer supplementary questions from the teacher and external examinator on definitions and results from the course syllabus

Subject overview
Hilbert spaces. Fourier series and Fourier integrals. Introduction to Banach Space Theory. The Banach-Steinhaus theorem. The open mapping theorem. The Hahn-Banach extension theorem. The representation theorem of Riesz for positive linear functionals on C(K).

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. Mandatory assignments. Pass/fail, internal assessment by teacher (2,5 ECTS)
2. Oral exam. Danish 7-mark scale, external marking (2,5 ECTS)

Reexamination in the same exam period or immediately thereafter.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours

Educational activities Study phase: 10 hours

This course is taught and evaluated together with MM543.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.