Department Mathematik



Lecture Course: Functional Analysis

Mon, Wed 14 - 16 in B 005


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)