Up: Teaching (past)


Lecture Course: Functional Analysis

Mon, Wed 14 - 16 in B 005


NEWS

  • (20/02/09)   Exams / Certificates

    28 out of 42 participants of the exam on 07/02/09 have passed the course. You can pick up your exam and, if applicable, your certificate in the office of Mrs Höchst (Room 330), beginning Wed, 25 Feb 09. Please note that Bachelor students are not allowed to take their exam home.

  • (29/01/09)   "Funktionalanalysis II" (4+2 hours/week) in Summer 09

    This course will be continued next semester. Among others, we will cover the following topics
    • spectral theory of bounded self-adjoint operators
    • unbounded operators, in particular symmetric operators, quadratic forms,...
    • spectral theory of unbounded operators
    • Fourier transformation

  • (19/01/09)   Note on Exercise 40 on Problem Sheet 12

    The operators S and T are both linear. Invertibility of S means that S, as given, is bijective.

  • (14/01/09)   Correction of Theorem 4.23

    Due to the problem with Theorem 4.23 which came up in class today, I modified Definition 4.21 and Theorem 4.23 (which is now 4.22). Examples 4.22 now come after the theorem as Remark 4.23. Please see the updated version with the definition of reflexivity as part of Theorem 4.22.

  • (09/01/09)   Correction of Remark 2.37

    The previous statement in part (b) on the inclusion of dual spaces requires a dense(!) subspace Y. The conclusion in part (c) was wrong! Please see the updated Remark 2.37 at the end of Sec. 2.4.
     
  • (13/11/08) Correction of Lemma 1.64

    Statement (iv) of Lemma 1.64, which was stated without proof in class, is not true under the hypotheses of the Lemma. (Thanks for pointing it out!) In fact, statement (iv) is a mere reformulation of statement (iv) of Lemma 65. Therefore it is equivalent to the validity of Baire's theorem. Please see the corrected version of Section 1.7 below. In case this has affected your solution of Problem 16 (which is the proof of Lemma 1.65), you will still get full credit, of course. The proof of Lemma 1.65 is now also available in the script (p. 40).
     
  • (24/10/08) Handing in of solutions to problem sheets

    Please note that you MUST hand in your solutions in teams of two (neither one, nor three or more). We have absolutely no capacity to correct more homework. Single returns will not be corrected from problem sheet 2 on.
     
  • (22/10/08) Comment on Exercise 8 – Problem Sheet 2:

    Since we have not "officially" introduced normed spaces so far, here is a reformulation of the problem. Prove that the space co, when equipped with the metric d, as defined in class, is a separable metric space.

Literature

The course will not follow a particular textbook. The following list provides a short selection of English and German textbooks on the subject (of which there are many!). Most of them cover the material of a two-semester course. One copy of each of the books listed below is kept on reserve in the library on a separate shelf for our course.

  • M Reed and B Simon, Methods of modern Mathematical Physics I: Functional analysis, Academic Press, 1980

    excellent textbook with a focus on spectral theory, beginning not very gentle, proofs sometimes a bit brief, unfortunately rather pricey

  • D Werner, Einführung in die Funktionalanalysis, Springer,

    a German classic, covers a broad range of topics, including historical remarks

  • M Dobrowolski, Angewandte Funktionalanalysis, Springer, 2006

    the basics of functional analysis plus a thorough discussion of Sobolev spaces and elliptic PDE's

  • E Kreyszig, Introductory functional analysis with applications, Wiley, 1978

    thorough and pedagogical, very explicit proofs, does not cover all topics treated in the course (e.g. no Lp-spaces)

  • P D Lax, Functional Analysis, Wiley, 2002

    well readable with an emphasis on spectral theory and some applications to quantum mechanics

  • F Hirzebruch and W Scharlau, Einführung in die Funktionalanalysis, BI Mannheim, 1971

    another German classic, elegant but very(!) concise