Lecture Course: Functional Analysis

Mon, Wed 14 - 16 in B 005

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 L^p-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)