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Functional Analysis (Winter Semester 2014/15)

This webpage is not maintained anymore. Updated informations concerning this lecture you find in the Studierendenportal of the KIT.

Schedule
Lecture: Tuesday 9:45-11:15 Nusselt-Hörsaal Begin: 21.10.2014
Wednesday 11:30-13:00 Criegee HS (R104)
Wednesday 11:30-13:00 SR 1. OG
Problem class: Friday 14:00-15:30 Eiermann Begin: 24.10.2014
Lecturers
Lecturer Prof. Dr. Roland Schnaubelt
Office hours: Wednesday, 11:30 - 13:00, and by appointment
Room 2-047 (Englerstr. 2) Kollegiengebäude Mathematik (20.30)
Email: schnaubelt@kit.edu
Problem classes Dr. Heiko Hoffmann
Office hours: Monday, 16:00 - 17:00, and by appointment
Room 2.048 Kollegiengebäude Mathematik (20.30)
Email: heiko.hoffmann@kit.edu

The lecture is concerned with Banach and Hilbert spaces as well as linear operators acting on these spaces. Typical examples are spaces of continuous and integrable functions and linear maps, which one defines via integration of such functions. In this way one can formulate integral equations as affine or linear equations on a suitable Banach space, and one can solve them by means of functional analytic methods. This class of problems was in fact the historical starting point for the development of functional analysis around 1900. In the following years it became a fundamental area of modern analysis and its applications in- and outside of mathematics. A preliminary list of topics:

  • basic properties and examples of metric and Banach spaces and of linear operators
  • principle of uniform boundedness and open mapping theorem
  • dual spaces, Hilbert spaces and Theorem of Hahn-Banach
  • weak convergence and Theorem of Banach-Alaoglu
  • Fourier transform, Sobolev spaces, distributions, and applications to partial differential equations

Prerequisites: Analysis 1-3 and Linear Algebra 1+2. The lecture is given in English.


Examination

There will be a written exam on 10 March 2015 from 11:00 to 13:00 in the Gerthsen lecture hall. More details will be given later.

Details concerning the written exam:

  • The written exam will take place on on 10 March 2015 from 11:00 to 13:00 in the Gerthsen lecture hall. If you want to take the examination, be already present at 10:45 please, so that the exam can begin on time.
  • If you want to take the examination, please register for the exam, depending on your branch of study and subject area, using the QISPOS system or contact Ms. Fuchs or Heiko Hoffmann. Closing date for registration is 02 March 2015.
  • The content of the exam will consist of the content of the chapters 1-4.
  • Apart from two handwritten DIN A4 pages (or equivalently: one double-page handwritten DIN A4 sheet of paper), there are no other auxiliary means allowed.
  • If you have further questions, please contact Heiko Hoffmann.

References

On my webpage one can find the PDF file of the manuscript of my lecture Functional Analysis from winter semester 2011/12. An updated version will be delivered probably in spring. A few relevant monographs.

  • D. Werner: Funktionalanalysis. Springer.
  • H.W. Alt: Lineare Funktionalanalysis. Springer.
  • H. Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer.
  • J.B. Conway: A Course in Functional Analysis. Springer.
  • M. Schechter: Principles of Functional Analysis. Academic Press.
  • A.E. Taylor, D.C. Lay: Introduction to Functional Analysis. Wiley.