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 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)