MM514: Hilbert- and Banach Spaces (5 ECTS)

STADS: 13006601

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
2nd quarter.

Teacher responsible
Email: szymanski@imada.sdu.dk

Timetable
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Revison of timetable:
: Skemaændringer efter ønske

Comment:
Ubegrænset deltagerantal. 2. kvartal. Fælles undervisning med MM815

Prerequisites:
None

Academic preconditions:
The content of the courses MM501 Calculus I, MM502 Calculus II, MM505 Linear Algebra, MM508 Topology I, MM509 Topology II, and MM517 Measure and Integration Theory must 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:
a) Mandatory exercises, pass/fail, internal evaluation by teacher. The exercises must be passed in order to take the oral exam.
(b) Oral exam. Danish 7 mark scale, external examiner.

Reexamination after 4th quarter.

Expected working hours
The teaching method is based on three phase model.

(a) Forelæsninger: 28 timer
(b) Eksaminatorier/opgaveregning: 14 timer
Educational activities

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.