Specialised Course in Linear Functional Analysis
Fördjupningskurs till lineär funktionalanalys

MATP45F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-09-24

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: MATP45
Undervisningsspråk: English

Syfte

The main goal of the course is to give a presentation of relevant applications of the abstract principles of functional analysis to a large variety of problems in mathematical analysis.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• be able to analyse problems in mathematical analysis using methods from functional analysis,
• be able to give examples of important applications of the abstract methods and principles of functional analysis,
• be able to give a detailed account of the theory behind methods described in the course,
• be able to give an account for research aspects within the subject and relate it to relevant problems within an independent work.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• be able to critically and systematically integrate knowledge from different areas of mathematical analysis to analyze and solve complex problems using the principles of functional analysis,
• be able to independently identify, formulate and solve relevant problems, as well as to plan and execute qualified tasks within a given time frame.

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• be able to argue for the important role of the principles of functional analysis in different areas of research in mathematics and physics,
• be able to identify their own need for further knowledge and take responsibility for developing their own knowledge.

Kursinnehåll

The course treats applications of - the Hahn-Banach theorem, weak convergence and compactness, - the Riesz representation theorem, - the use of orthonormal bases, - boundedness, compactness and spectra of integral operators, - the spectral theorem for compact, self-adjoint operators.

Kurslitteratur

Lax, Peter D.: Functional Analysis. John Wiley & Sons, 2002. ISBN 9780471556046.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, seminarier

Kursens examination

Examinationsform: övrigt. The examination consists of oral presentations of solutions of problems or proofs of relevant results during the course and a problem-solving project at the end of the course.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: The postgraduate student is assumed to have knowledge corresponding to MATP35F Linear Functional Analysis or be studying that course in parallel with MATP45F.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.ctr.maths.lu.se/course/MATP45/